Specific Heat Capacity

Q. If $C_P$ and $C_V$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

1. $C_P-C_V=\frac{R}{28}$
2. $C_P-C_V=\frac{R}{14}$
3. $C_P-C_V=R$
4. $C_P-C_V=28R$

Q. A gas mixture contains $1\text{g}{H}_2$ and $1\text{g He}$. If temperature of gas mixture is increased from $0^{\circ }C$ to ${100}^{\circ }C$ at isobaric process, then find the heat given to the gas mixture. $[{\gamma }_{He}=\frac{5}{3},{\gamma }_{He}=\frac{7}{5},R=2\text{cal/mol-K}]$

1. $124\text{cal}$
2. $327\text{cal}$
3. $218\text{cal}$
4. $475\text{cal}$

Q. Thermal capacity of $20\text{g}$ of copper is (Given:Specific heat $=0.1\text{cal/g-K}$)

1. $2\text{cal}/{}^{\circ }\text{C}$
2. $2\text{cal/ K}$
3. $8.4\text{J/K}$
4. All of the above

Q. Two liquid with masses $m_1=10\text{kg}$ and $m_2=20\text{kg}$ are thoroughly mixed. If there specific heats are $C_1=0.2{\text{cal/g -}}^{\circ }\text{C}$ and $C_2=0.1{\text{cal/g -}}^{\circ }\text{C}$ and their temperatures are ${30}^{\circ }\text{C}$ and ${40}^{\circ }\text{C}$ respectively, then the final temperature of the mixture is

1. ${25}^{\circ }\text{C}$
2. ${35}^{\circ }\text{C}$
3. ${30}^{\circ }\text{C}$
4. ${28}^{\circ }\text{C}$

Q. A tank with a movable piston having initial volume of $0.2{\text{m}}^3$ contains $He$ gas at a temperature of $300\text{K}$ and pressure ${10}^5{\text{N/m}}^2$. Find the amount of heat required to raise the temperature of gas to $400\text{K}$ at constant pressure. The molar heat capacity of $He$ at constant pressure is $5{\text{cal K}}^{-1}{\text{mol}}^{-1}$.

1. $2400\text{cal}$
2. $3800\text{cal}$
3. $4000\text{cal}$
4. $5000\text{cal}$

Q. $5\text{kJ}$ of heat is required to raise the temperature of $10\text{moles}$ of a gas by ${100}^{\circ }\text{C}$, at a constant volume. The specific heat capacity of the gas is $\left(\text{in J/ mol-K}\right)$

1. $5$
2. $25$
3. $10$
4. $13.4$

Q.

540 g of ice at $0^{\circ }C$ is mixed with 540 g of water at ${80}^{\circ }C$. The final temperature of the mixture is

1. $0^{\circ }C$

2. ${40}^{\circ }C$

3. ${80}^{\circ }C$

4. Less than $0^{\circ }C$

Q. A liquid of mass m and specific heat c is heated to a temperature 2T. Another liquid of mass m/2 and specific heat 2c is heated to a temperature T. If these two liquids are mixed, the resulting temperature of the mixture is

1. $\left(\frac{2}{3}\right)T$
2. $\left(\frac{8}{5}\right)T$
3. $\left(\frac{3}{5}\right)T$
4. $\left(\frac{3}{2}\right)T$

Q. Two spheres made of the same substance have diameters in the ratio $1:2$. Their thermal capacities are in the ratio of:

1. $1:8$
2. $1:4$
3. $1:16$
4. $1:32$

Q. Which of the following is the correct unit for heat capacity?

1. ${\text{JK}}^{-1}{\text{kg}}^{-1}$
2. ${\text{JK}}^{-1}$
3. ${\text{Jkg}}^{-1}{{}^{\circ }\text{C}}^{-1}$
4. ${\text{JK}}^{-1}{\text{kg}}^{-1}$

Q. $5\text{kJ}$ of heat is required to raise the temperature of $10\text{moles}$ of a gas by ${100}^{\circ }\text{C}$, at a constant volume. The specific heat capacity of the gas is $\left(\text{in J/ mol-K}\right)$

1. $5$
2. $25$
3. $10$
4. $13.4$

Q. The specific heat capacity of a metal is $0.01{\text{cal/g}}^{\circ }\text{C}$. If heat capacity of $m\text{kg}$ of metal is $0.42\text{J}{/}^{\circ }\text{C}$. Find the value of $m$.

1. ${10}^{-2}$
2. ${10}^{-1}$
3. $1$
4. ${10}^{-3}$

Q. A calorimeter of water equivalent $5\times {10}^{-3}kg$ contains $25\times {10}^{-3}kg$ of water. It takes 3 minutes to cool from ${28}^{\circ }C$ to ${21}^{\circ }C$. When the same calorimeter is filled with $30\times {10}^{-3}kg$ of turpentine oil, then it takes 2 minutes to cool from ${28}^{\circ }C$ to ${21}^{\circ }C$. Find the specific heat of turpentine oil.

1. $1.5Jk{g}^{-1}\circ C^{-1}$
2. $0.5Jk{g}^{-1}\circ C^{-1}$
3. $45Jk{g}^{-1}\circ C^{-1}$
4. $5Jk{g}^{-1}\circ C^{-1}$

Q.

When there is no change of state in a process, which of the following is not required to calculate the heat lost or gained in the process?

1. Weight

2. Specific heat

3. Relative density

4. Temperature change

Q. Heatis being supplied to a homogeneous material at a uniform rate and its temperature is plotted against time.


Which of the following options hold true for the specific heat capacity of the material?

1. Specific heat capacity is greater in solid state than in liquid state.
2. Specific heat capacity is greater in liquid state than in solid state.
3. Specific heat capacity is equal in both liquid state and in solid state and is equal to zero.
4. Specific heat capacity is equal in both liquid state and in solid state and is equal to infinity.

Q. A metallic sphere of radius $r$ and specific heat $S$ is rotated about an axis passing through its centre of mass at an angular speed of $n$ rotations per second. It is suddenly stopped and $50\%$ of its energy is used in increasing its temperature. Then, the rise in temperature of the sphere is

1. $\frac{2{\pi }^2{n}^2{r}^2}{5S}$
2. $\frac{{\pi }^2{n}^2}{10r^{2}S}$
3. $\frac{7}{8}\pi r^2{n}^{2}S$
4. $\frac{5(\pi rn{)}^2}{14S}$

Q. The specific heat of argon at constant volume is $0.075\text{kcal/kg K}$. Calculate its atomic weight [ $R=2\text{cal/mol K}$ ]

1. $40\text{gram/mole}$
2. $70\text{gram/mole}$
3. $60\text{gram/mole}$
4. $25\text{gram/mole}$

Q. One mole of an ideal monoatomic gas undergoes a process described by the equation $P{V}^3=\text{constant}$. The molar heat capacity of this gas during this process is

1. $\frac{3}{2}R$
2. $\frac{5}{2}R$
3. $2R$
4. $R$

Q. The specific heat of a substance varies with temperature according to the function $S=0.20+0.14T+0.023T^2$ with $T$ in ${}^{\circ }\text{C}$ and $S$ in ${\text{cal/g}}^{\circ }\text{C}.$ What is the energy required to raise the temperature of $2.0\text{g}$ of this substance from $5^{\circ }\text{C}$ to ${15}^{\circ }\text{C}$?

1. $50\text{cal}$
2. $82\text{cal}$
3. $107\text{cal}$
4. $230\text{cal}$

Q. Three liquids with masses $m_1,m_2,m_3$ are thoroughly mixed, If their specific heats are $c_1,c_2,c_3$ and their temperatures $T_1,T_2,T_3$ respectively, then the temperature of the mixture is

1. $\frac{c_1{T}_1+c_2{T}_2+c_3{T}_3}{m_1{c}_1+m_2{c}_2+m_3{c}_3}$
2. $\frac{m_1{c}_1{T}_1+m_2{c}_2{T}_2+m_3{c}_3{T}_3}{m_1{c}_1+m_2{c}_2+m_3{c}_3}$
3. $\frac{m_1{c}_1{T}_1+m_2{c}_2{T}_2+m_3{c}_3{T}_3}{m_1{T}_1+m_2{T}_2+m_3{T}_3}$
4. $\frac{m_1{T}_1+m_2{T}_2+m_3{T}_3}{c_1{T}_1+c_2{T}_2+c_3{T}_3}$

Q. $200\text{g}$ of ice at $-{20}^{\circ }\text{C}$ is mixed with $500\text{g}$ of water at ${20}^{\circ }\text{C}$ in an insulating vessel. What is the final mass of water in the vessel? (Specific heat of ice $=0.5{\text{cal g}}^{-1}$${}^{\circ }{C}^{-1}$).

1. $700\text{g}$
2. $600\text{g}$
3. $400\text{g}$
4. $200\text{g}$

Q. An object of mass $8\text{kg}$ falls through a height of $60\text{m}$ and by means of a mechanical linkage, rotates a paddle wheel that stirs $0.8\text{kg}$ of water. Determine the change in temperature of water if initial temperature was ${15}^{\circ }\text{C}$. Assume no heat is lost to surroundings, specific heat of water, $c=4190\text{J/kg}{}^{\circ }\text{C})$.

1. ${0.5}^{\circ }\text{C}$
2. ${1.4}^{\circ }\text{C}$
3. ${2.1}^{\circ }\text{C}$
4. ${3.6}^{\circ }\text{C}$

Q. Two spheres $A$ and $B$ have diameters in the ratio $1:2$, densities in the ratio $2:1$ and thermal capacities in the ratio $1:12$. Find the ratio of their specific heat capacities.

1. $1:6$
2. $1:12$
3. $1:3$
4. $1:4$

Q. Thermal capacity of $20\text{g}$ of copper is (Given:Specific heat $=0.1\text{cal/g-K}$)

1. $2\text{cal}/{}^{\circ }\text{C}$
2. $2\text{cal/ K}$
3. $8.4\text{J/K}$
4. All of the above

Q. The amount of heat needed to increase the temperature of $1\text{gm}$ of water from ${14.5}^{\circ }\text{C}$ to ${15.5}^{\circ }\text{C}$ at one atmospheric pressure is:

1. $1\text{calorie}$
2. $4.2\text{calorie}$
3. $1\text{joule}$
4. $42\text{calorie}$

Q. $50g$of copper is heated to increase its temperature by${10}^{0}C.$If the same quantity of heat is given to$10g$of water, the rise in its temperature is.$(specificheatofcopper=420J{K}^{-1}oC-1)$

1. $5^{\circ }C$
2. $6^{\circ }C$
3. $7^{\circ }C$
4. $8^{\circ }C$

Q. How much heat energy is released when $10\text{kg}$ of liquid water at ${100}^{\circ }\text{C}$ is brought to its freezing point?
(Specific heat of water $=1{\text{cal/g}}^{\circ }\text{C}$)

1. $2100\text{kJ}$
2. $420\text{kJ}$
3. $4200\text{kJ}$
4. $8400\text{kJ}$

Q. Which of the following statements is/are correct?
(i) The specific heat capacity at constant temperature is infinite.
(ii) When no heat is added and the temperature is variable, specific heat capacity is equal to zero.

1. only (i) is correct
2. only (ii) is correct
3. both (i) and (ii) are correct
4. none of the statements is correct

Q. An object of mass $8\text{kg}$ falls through a height of $60\text{m}$ and by means of a mechanical linkage, rotates a paddle wheel that stirs $0.8\text{kg}$ of water. Determine the change in temperature of water if initial temperature was ${15}^{\circ }\text{C}$. Assume no heat is lost to surroundings, specific heat of water, $c=4190\text{J/kg}{}^{\circ }\text{C})$.

1. ${0.5}^{\circ }\text{C}$
2. ${1.4}^{\circ }\text{C}$
3. ${2.1}^{\circ }\text{C}$
4. ${3.6}^{\circ }\text{C}$

Q. An engine operates by taking a monoatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to ______.