Molar and Specific Heat Capacity

Q. One mole of a real gas at its critical temperature has a relation between its pressure (in atm) and volume (in litres) as follows:
$P=\frac{2R{T}_c}{V}-\frac{3X}{V^2}+\frac{Y}{V^3}$
Where $T_c$ is the critical temperature (in K) and R is the gas constant while X and Y are some constants. Find the correct option(s) about the gas and its given relation.

1. The unit of the constant X is $atmL$
2. The unit of the constant Y is atm $atm{L}^3$
3. $T_c=\frac{3X^2}{2RY}$
4. At critical volume $\frac{dP}{dV}=0$

Q. Equal volumes of two monoatomic gases, A and B at same temperature and pressure are mixed. The ratio of specific heats $\frac{C_p}{C_v}$ of the mixture will be:

1. 0.83
2. 1.5
3. 3.3
4. 1.67

Q. At constant volume, the specific heat of a gas is 0.025 $cal{K}^{-1}{g}^{-1}$ and its molecular weight is 120 $gmo{l}^{-1}$. The atomicity of the gas is:
Given: R = 2 cal $K^{-1}mo{l}^{-1}$

1. Diatomic
2. Triatomic
3. Monoatomic
4. None of the above

Q.

For an ideal gas $(\frac{C_P}{C_v}=\gamma )$; of molar mass M, its specific heat capacity at constant volume is:

1. $\frac{\gamma R}{(\gamma -1)M}$

2. $\frac{\gamma }{M(\gamma -1)}$

3. $\frac{M}{R(\gamma -1)}$

4. $\frac{\gamma RM}{(\gamma -1)}$

Q. For a reaction, 2A(g) + B(g) → 4C(g), if ΔU = 12 kJ and ΔS = 60 JK^–1 at 27ºC then ΔG will be

अभिक्रिया 2A(g) + B(g) → 4C(g) के लिए, यदि 27°C पर ΔU = 12 kJ तथा ΔS = 60 JK^–1 है, तो ΔG होगा

1. –7.25 kJ
2. –1.72 kJ
3. –3.51 kJ
4. –9.12 kJ

Q. Consider a system containing one mole of a diatomic gas, contained by a piston. What is the temperature change of the gas, if $q=50J$ and $W=-100J?$
(Given $C_v=\frac{5}{2}R$ )

1. $-50K$
2. $-2.4K$
3. $-5.8K$
4. $-1.25K$

Q. A $140W$ heater was placed in $2.00kg$ of methanol $\left(C{H}_{3}OH\right)$ and turned on for exactly 2 min. The temperature increased by $4.24K$. Assuming that all the heat is absorbed by methanol, then molar heat capacity of methanol is

1. $81.4Jmo{l}^{-1}{K}^{-1}$
2. $36.50Jmo{l}^{-1}{K}^{-1}$
3. $9.0Jmo{l}^{-1}{K}^{-1}$
4. $63.4Jmo{l}^{-1}{K}^{-1}$

Q. The molar heat capacity ( $C_p$) of water at constant pressure is 75 $J{K}^{-1}mol{e}^{-1}$. The increase in temperature (in K) of 100 g of water when 2kJ of heat is supplied to it is:

1. 2.4 K
2. 3.6 K
3. 4.8 K
4. 5.2 K

Q.

Rate of disappearance of the reactant A in the reversable and one step reaction $A\rightleftharpoons B$ at two temperatures is given by
$\frac{-d\left[A\right]}{dt}=2.0\times {10}^{-3}{s}^{-1}\left[A\right]-5.0\times {10}^{-4}{s}^{-1}\left[B\right]\left(at{27}^{\circ }C\right)\frac{-d\left[A\right]}{dt}=8.0\times {10}^{-2}{s}^{-1}\left[A\right]-4.0\times {10}^{-3}{s}^{-1}\left[B\right]\left(at{127}^{\circ }C\right)$
The enthapy of the reaction in the given temperature range is

1. $-\frac{2.303\times 8.314\times 300\times 400}{100}log5J$

2. $\frac{2.303\times 8.314\times 300\times 400}{100}log50J$

3. $\frac{2.303\times 8.314\times 300\times 400}{100}log5J$

4. $\frac{100}{2.303\times 8.314\times 300\times 400}log5J$

Q. A diatomic ideal gas initially at $273K$ is given $100cal$ heat due to which system did $209J$ work. Molar heat capacity $\left(C_m\right)$ of gas for the process is:

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