Specific Heat Capacity

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. $R$
4. $2R$

Q. The volume $V$ of a monoatomic gas varies with its temperature $T$ as shown in the graph. The ratio of work done by the gas to the heat absorbed by it when it undergoes a change from state A to state B is

1. $\frac{2}{5}$
2. $\frac{2}{7}$
3. $\frac{1}{3}$
4. $\frac{2}{3}$

Q.

$1$ mole of a rigid diatomic gas performs a work of $Q/5$ when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{\mathrm{x}}{8}R$. The value of x is _________.

Q. Work done in converting one gram of ice at $-{10}^{\circ }\text{C}$ into steam at ${100}^{\circ }\text{C}$ is -
[Given, specific heat of ice $c_i=0.5{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$, specific heat of water $c_w=1{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$, latent heat of fusion of ice $L_f=80\text{cal/g}$, & latent heat of vaporization of steam $L_v=540\text{cal/g}$]

1. $3045\text{J}$
2. $5023\text{J}$
3. $1128\text{J}$
4. $725\text{J}$

Q. A cylinder of radius $R$ is surrounded by a cylinder shell of inner radius $R$ and outer radius $2R$. The thermal conductivity of the material of the cylinder is $K_1$ and that of the outer cylinder is $K_2$. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is:

1. $\frac{K_1+3K_2}{4}$
2. $\frac{K_1+K_2}{2}$
3. $\frac{3K_1+K_2}{4}$
4. $K_1+K_2$

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

Q.

Does Latent heat change with pressure?

Q. $1c{m}^3$ of water at its boiling point absorbs 540 calories of heat to become steam with a volume of $1671c{m}^3.$ If the atmospheric pressure is $1.013\times {10}^{5}N/m^2$ and the mechanical equivalent of heat = 4.19 J/calorie, the energy spent in this process in overcoming intermolecular forces is

1. 540 calorie
2. Zero
3. 40 calorie
4. 500 calorie

Q. Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies, with time, is graphically represented as shown in the figure. The ratio of specific heat capacities is :


Temp T(°C) Time (f min.) 

Q.

What is the heat required to raise the temperature of a body by $1°\mathrm{C}$ called?

Q. Two thermometers X and Y have ice points marked at ${15}^{\circ }$ and ${25}^{\circ }$ and steam points marked as ${75}^{\circ }$ and ${125}^{\circ }$ respectively. When thermometer X measures the temperature of a bath as ${60}^{\circ }$ on it, what would thermometer Y read when it is used to measure the temperature of the same bath?

1. ${100}^{\circ }$
2. ${90}^{\circ }$
3. ${60}^{\circ }$
4. ${75}^{\circ }$

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. Statement 1: Heat capacity/Thermal capacity of a substance depends on mass of substance.
Statement 2: Specific heat capacity of a substance is independent of mass of substance.

1. Statement 1 is correct, statement 2 is incorrect.
2. Both statements are incorrect.
3. Statement 1 is incorrect, statement 2 is correct.
4. Both statements are correct.

Q. The thermal capacity of $100\text{g}$ of aluminum (specific heat $=0.2{\text{cal/g}}^{\circ }\text{C})$ is

1. $0.002{\text{cal/}}^{\circ }\text{C}$
2. $20{\text{cal/}}^{\circ }\text{C}$
3. $200{\text{cal/}}^{\circ }\text{C}$
4. $100{\text{cal/}}^{\circ }\text{C}$

Q. When an ideal diatomic gas is heated at a constant pressure, what fraction of heat energy supplied is used in doing work?

Q. Two successive resonance frequencies in an open organ pipe are $1800\text{Hz}$ and $2600\text{Hz}$. Find the length of the tube if the speed of sound in air is $340\text{m/s}$.

1. $21.25\text{cm}$
2. $20\text{cm}$
3. $20.5\text{cm}$
4. $22.25\text{cm}$

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

Q.

An ideal gas occupies a volume of $2{\mathrm{m}}^3$ at a pressure of $3\times {10}^6\mathrm{Pa}$. The energy of the gas is:

Q.

Under steady state, the temperature of a body

1. Does not change with time and is same at all the points of the body

2. Increases with time

3. Decreases with time

4. Does not change with time but is different at different points of the body

Q. The heat capacity of object A is is twice the object B .initially B is at 300K and A is at 450. They are placed in thermal contact and the combination is isolated.the final temperature of both object is

Q.

An ideal diatomic gas under goes a process in which it internal energy changes with volume as given $U=c{V}^{\frac{2}{5}}$ where c is constant. Find the ratio of molar heat capacity of the process to universal gas constant R.___

Q. A perfect gas at ${27}^{\circ }C$ is heated at constant pressure to ${327}^{\circ }C$. If original volume of gas at ${27}^{\circ }C$ is V then volume at ${327}^{\circ }C$ is

1. V
2. 3V
3. 2V
4. V/2

Q. Two identical beakers $A$ and $B$ contain equal volumes of two different liquids at ${60}^{\circ }C$ each and left to cool down. Liquid in $A$ has density of $8\times {10}^{2}kg/m^3$ and specific heat of $2000Jk{g}^{-1}{K}^{-1}$ while liquid in $B$ has density of ${10}^{3}kg{m}^{-3}$ and specific heat of $4000Jk{g}^{-1}{K}^{-1}$. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same?

1. 
2. 
3. 
4. 

Q. A quantity of an ideal monoatomic gas consists of $n$ moles initially at temperature $T_1$. The pressure and volume both are then slowly doubled in such a manner that the process traces out a straight line on a $P-V$ diagram. The ratio $\frac{Q}{nR{T}_1}$ for the given thermodynamic process is equal to:
(Q is the heat supplied to the gas)

1. $1.5$
2. $6$
3. $4.5$
4. $3$

Q. Define latent heat of vaporization.

Q.

Conduction of heat is not possible through gases. Why?

1. Gas molecules are very loosely packed.

2. Gas molecules possess vibratory, rotatory and translatory motions.

3. Gas molecules possess very high kinetic energy.

4. Gas molecules are highly diffusible

Q. Two cylinders contain same amount of ideal monatomic gas. Same amount of heat is given to two cylinders. if temperature rise in cylinder A is $T_o$ then temperature rise in cylinder B will be

1. $2T_o$
2. $\frac{T_o}{2}$
3. $\frac{4}{3}{T}_o$
4. $\frac{5}{3}{T}_o$

Q.

A 50 kg man is running at a speed of 18 km $h^{-1}$. If all the kinetic energy of the man can be used to increase the temperature of water from ${20}^0$ C to ${30}^0$ C, how much water can be heated with this energy ?

Q. If P-V diagram of a diatomic gas is plotted, it is a straight line passing through origin. The molar heat capacityof the gas in the process is $nR$, where $n$ is an integer, then the value of $n$ is

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