Heat Capacity

Q. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_p/C_{\nu }$ for the gas is

1. 
2. 
   
3. 
   
   
4. 
   
   

Q.

4.0 g of a gas occupies 22.4L at NTP. The specific heat capacity of the gas at constant volume is 5.0 JK-1mol-1. If the speed of sound in the gas at NTP is 952 ms-1, then the heat capacity at constant pressure is.

(Take gas constant R=8.3 JK-1mol-1)

1. 7.5 JK-1mol-1
2. 8.0 JK-1mol-1
3. 87.5 JK-1mol-1
4. 7.0 JK-1mol-1

Q. $70\text{cal}$ of heat is required to raise the temperature of $2$ moles of an ideal gas at constant pressure from ${30}^{\circ }\text{C}$ to ${35}^{\circ }\text{C}$. The amount of heat required to raise the temperature of the same gas through same range of temperature (${30}^{\circ }\text{C}$ to ${35}^{\circ }\text{C}$) at constant volume is
Given $(\gamma =7/5)$

1. $30\text{cal}$
2. $50\text{cal}$
3. $70\text{cal}$
4. $90\text{cal}$

Q. Two moles of a monoatomic gas is mixed with three moles of a diatomic gas. The molar specific heat of the mixture at a constant volume is

1. $1.6R$
2. $3.6R$
3. $2.1R$
4. $6.25R$

Q. A gaseous mixture consists of $16\text{g}He$ and $16\text{g}{O}_2$. The ratio of specific heats $\frac{C_p}{C_v}$ of the mixture is

1. $1.54$
2. $1.59$
3. $1.62$
4. $1.4$

Q. One mole of a monoatomic ideal gas undergoes the process $A\to B$ in the given $P-V$ diagram. The specific heat for this process is

1. $3R/2$
2. $13R/6$
3. $5R/2$
4. $2R$

Q. When an ideal monoatomic gas is heated at constant pressure, the fraction of heat energy supplied which increases the internal energy of gas is

1. $3/5$
2. $3/7$
3. $3/4$
4. $2/5$

Q. A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, $C_v=2R$ . Here, $R$ is the gas constant. Initially, each side has a volume $V_0$ and temperature $T_0$. The left side has an electric heater, which is turned on at very low power to transfer heat $Q$ to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to $V_0/2$. Consequently, the gas temperatures on the left and the right sides become $T_L$ and $T_R$, respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.

The value of $\frac{T_R}{T_0}$ is

1. $\sqrt{2}$
2. $\sqrt{3}$
3. $2$
4. $3$

Q.

In the circuit shown, initially there is no charge on capacitors and keys $S_1$ and $S_2$ are open. The values of the capacitors are $C_1=10\mu F$, $C_2=30\mu F$, and $C_3=C_4=80\mu F$. Which statements is/are correct?

1. If key $S_1$ is kept closed for long time such that capacitors are fully charged, the voltage across the capacitor $C_1$ will be $4V$.
2. The key $S_1$ is kept closed for long time such that capacitors are fully charged. Now key $S_2$ is closed, at this time, the instantancous current across $30\Omega$ resistor (between points $P$ and $Q$ ) will be $0.2A$ (round off to $1^{\text{st}}$ decimal place).
3. At time $t=0,$ the key $S_1$ is closed, the instantaneous current in the closed circuit will be $25mA.$
4. If key $S_1$ is kept closed for long time such that capacitors are fully charged, the voltage difference between point $P$ and $Q$ will be $10V$.

Q. One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is

1. 2R
2. 2.5 R
3. 635043695927768708_1459389.PNG
4. 8

Q.

An ornament weighing 36 g in air, weighs only 34 g in water. Assuming that some copper is mixed with gold to prepare the ornament, find the amount of copper in it. Specific gravity of gold is 19.3 and that of copper is 8.9.

Q.

The graph shown in the figure represents change in the temperature of $5kg$ of a substance with time, as it absorbs heat at a constant rate of $42kJ$ $mi{n}^{-1}$. The latent heat of vapourization of the substance is:

1. $630kJk{g}^{-1}$
2. $126kJk{g}^{-1}$
3. $84kJk{g}^{-1}$
4. $12.6kJk{g}^{-1}$

Q. The pressure $P$ of an ideal diatomic gas varies with its absolute temperature $T$ as shown in the figure. The molar heat capacity of the gas during this process is:
[$R$ is the gas constant]

1. $1.7R$
2. $3.25R$
3. $2.5R$
4. $4.2R$

Q. If $c_p$ and $c_v$ denotes the specific heat of nitrogen at constant pressure and constant volume respectively, then

1. $c_p-c_v=28R$
2. $c_p-c_v=\frac{R}{28}$
3. $c_p-c_v=\frac{R}{14}$
4. $c_p-c_v=R$

Q. Heat capacity of a substance is infinite. It means

1. no change in temperature whether heat is taken in or given out
2. All of the above
3. heat is given out
4. heat is taken in

Q. A gaseous mixture enclosed in a vessel consists of one $\text{gram mole}$ of a gas $A$ with $\gamma =\frac{5}{3}$ and some amount of gas $B$ with $\gamma =\frac{7}{5}$ at a temperature $T$. The gases $A$ and $B$ do not react with each other and are assumed to be ideal. Find the number of moles of the gas $B$ if $\gamma$ for the gaseous mixture is $\left(\frac{19}{13}\right)$.

1. $1$
2. $2$
3. $3$
4. $4$

Q. Two moles of helium $\left(He\right)$ are mixed with four moles of hydrogen $\left(H_2\right)$. The molar heat capacity of the mixture at constant pressure is

1. $\frac{15R}{6}$
2. $\frac{3R}{2}$
3. $\frac{17R}{6}$
4. $\frac{19R}{6}$

Q. Find the change in internal energy in joules when 10 g of air is heated from ${30}^{\circ }C$ to ${40}^{\circ }C$. Given $C_v=0.172kcal/kgK$

Q.

The specific heat capacities of hydrogen at constant volume and at constant pressure 2.4 cal $g^{-1}{}^0{C}^{-1}$ and $3.4cal{g}^{-1}{}^0{C}^{-1}$ respectively. The molecular weight of hydrogen is 2 g $mo{l}^{-1}$ and the gas constant $R=8.3\times {10}^{\gamma }$ ~$er{g}^0{C}^{-1}mo{l}^{-1}.$ Calculate the valuve of J

Q. Suppose the distance between the atoms of a diatomic gas remains constant. Its specific heat at constant volume per mole is

1. $\frac{3R}{2}$
2. $\frac{7R}{2}$
3. $\frac{5R}{2}$
4. $\frac{9R}{2}$

Q. A gas at pressure p is adiabatically compressed so that its density becomes twice that of initial value. Given that $\gamma =C_P/C_v=7/5$ what will be the final pressure of the gas?

1. 2.63 p
2. p
3. 7/5 p
4. 2 p

Q. A solid material is supplied with heat at a constant rate. The temperature of material is changing with heat input as shown in the figure. What does slope DE represent.

1. Latent heat of liquid
2. Latent heat of vapour
3. Heat capacity of vapour
4. Inverse of heat capacity of vapour

Q. For a gas $\gamma =1.4$. Then atomicity, $C_p$ and $C_V$ respectively of the gas are

1. Monoatomic, $\frac{5R}{2},\frac{3R}{2}$
2. Monoatomic, $\frac{7R}{2},\frac{5R}{2}$
3. Diatomic, $\frac{7R}{2},\frac{5R}{2}$
4. Triatomic, $\frac{7R}{2},\frac{5R}{2}$

Q. Two closed vessels of equal volume contain air at 105 kPa, 300 K and are connected through a narrow tube.If one of the vessels is now maintained at 300 K and the other at 400 K, what will be the Pressure in the vessels ?

1. 220 kPA
2. 120 kPa
3. 235 kPa
4. 100 kPa

Q. $n_1$ and $n_2$ moles of two ideal gases of thermodynamics constant ${\gamma }_1$ and ${\gamma }_2$ respectively are mixed, for the mixture is –

1. 
2. 
3. 
4. 

Q. A gas for which $\gamma =1.5$ is suddenly compressed to the $\frac{1}{4}$ th of the initial volume. Then the ratio of the final to the initial pressure is

1. 1 : 8
2. 1 : 6
3. 1 : 4
4. 8 : 1

Q. The molar heat capacity of a gas at constant volume is $5{\text{cal mol}}^{-1}{\text{K}}^{-1}$. Find the value of $\gamma$ for the gas if the gas constant, $R=2{\text{cal mol}}^{-1}{\text{K}}^{-1}$.

1. $1.66$
2. $1.4$
3. $1.33$
4. $1.8$

Q. For an ideal gas, the slope of $V-T$ graph during an adiabatic process is $\frac{dV}{dT}=-m$ at a point where volume and temperature are $V_0$ and $T_0$. Find the value of $C_P$ of the gas. It is given that $m$ is a positive number.

1. $(\frac{m{T}_0}{V_0}+1)R$
2. $\frac{m{T}_{0}R}{V_0}$
3. $(\frac{-m{T}_0}{V_0}+1)R$
4. $\left(\frac{-m{T}_{0}R}{V_0}\right)$

Q.

Which of the substances A, B and C has the lowest heat capacity, if heat is supplied to all of them at equal rates? The temperature versus time graph is shown:

1. A

2. B

3. Equal for all

4. C

Q. Molar specific heat at constant volume for a non-linear triatomic gas ( neglect vibration of molecules) is:

1. $4R$
2. $R$
3. $2R$
4. $3R$