Kinetic Theory of Gases and ldeal Gas | Physics JEE previous year questions with Solutions

Q 1 :
The specific heat at constant pressure of a real gas obeying $P V^{2} = R T$ equation is: [2024]

$\frac{R}{3} + C_{v}$
$R$
$C_{v} + R$
$C_{v} + \frac{R}{2 V}$

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(D) $d Q = d U + d W$

$n C d T = n C_{v} d T + d W,$ We need to find $d W$

we have $P V^{2} = R T, P =$ constant

differentiating, $P 2 V d V = R d T \Rightarrow P d V = \frac{R . d T}{2 V}$

Also, $d W = P d V = \frac{R . d T}{2 V}$

For one mole of gas, $C . d T = C_{v} d T + \frac{R . d T}{2 V} \Rightarrow C = C_{v} + \frac{R}{2 V}$

Q 2 :
A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27°C). The ratio of specific heat of gases at constant volume respectively is [2024]

$\frac{3}{2}$
$\frac{7}{5}$
$\frac{3}{5}$
$\frac{5}{3}$

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(C) $\frac{{(C_{v})}_{m o n o}}{{(C_{v})}_{d i a}} = \frac{\frac{3}{2} R}{\frac{5}{2} R} = \frac{3}{5}$

Q 3 :
If three moles of monoatomic gas $(γ = \frac{5}{3})$ is mixed with two moles of a diatomic gas $(γ = \frac{7}{5})$ , the value of adiabatic exponent $γ$ for the mixture is [2024]

1.75
1.40
1.52
1.35

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(C) Monoatomic gas $\to 3$ mole

Diatomic gas $\to 2$ mole

$γ_{m i x} = 1 + \frac{2}{f_{m i n}}$ ....(1)

$f_{m i x} = \frac{n_{1} f_{1} + n_{2} f_{2}}{n_{1} + n_{2}} = \frac{3 (3) + 2 (5)}{5} = \frac{19}{5}$

$γ_{m i x} = 1 + \frac{2}{19 / 5} = 1 + \frac{10}{19} = \frac{29}{19}$

$γ_{m i x} = 1.53$

Q 4 :
A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is [2024]

29RT
20RT
27RT
21RT

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(C) $U = n C_{V} T$

$\Rightarrow U = n_{1} C_{V_{1}}$ $T + n_{2} C_{V_{2}} T$

$\Rightarrow 8 \times \frac{3 R}{2} \times T + 6 \times \frac{5 R}{2} \times T = 27 R T$

Q 5 :
Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is [2024]

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

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(A) $C_{V} = \frac{n_{1} C_{v_{1}} + n_{2} C_{v_{2}}}{n_{1} + n_{2}}$

$= \frac{2 \times \frac{3}{2} R + 6 \times \frac{5}{2} R}{2 + 6}$

$= \frac{9}{4} R$

Topic Question Set

Q 1 :
The specific heat at constant pressure of a real gas obeying $P V^{2} = R T$ equation is: [2024]

Q 2 :
A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27°C). The ratio of specific heat of gases at constant volume respectively is [2024]

Q 3 :
If three moles of monoatomic gas $(γ = \frac{5}{3})$ is mixed with two moles of a diatomic gas $(γ = \frac{7}{5})$ , the value of adiabatic exponent $γ$ for the mixture is [2024]

Q 4 :
A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is [2024]

Q 5 :
Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is [2024]

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Topic Question Set

Q 1 : The specific heat at constant pressure of a real gas obeying PV2=RT equation is: [2024]

Q 2 : A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27°C). The ratio of specific heat of gases at constant volume respectively is [2024]

Q 3 : If three moles of monoatomic gas (γ=53) is mixed with two moles of a diatomic gas (γ=75), the value of adiabatic exponent γ for the mixture is [2024]

Q 4 : A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is [2024]

Q 5 : Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is [2024]

Want Us to Email you About Special Offers & Updates?

Q 1 :
The specific heat at constant pressure of a real gas obeying $P V^{2} = R T$ equation is: [2024]

Q 2 :
A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27°C). The ratio of specific heat of gases at constant volume respectively is [2024]

Q 3 :
If three moles of monoatomic gas $(γ = \frac{5}{3})$ is mixed with two moles of a diatomic gas $(γ = \frac{7}{5})$ , the value of adiabatic exponent $γ$ for the mixture is [2024]

Q 4 :
A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is [2024]

Q 5 :
Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is [2024]