A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is [2023]

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Q.
A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is $(given, γ = \frac{3}{2})$ [2023]

1 $W = T R [\sqrt{2} - 2]$

2 $W = \frac{T}{R} [\sqrt{2} - 2]$

3 $W = \frac{R}{T} [2 - \sqrt{2}]$

4 $W = T R [2 - \sqrt{2}]$

Ans.
(4)

$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$

$T V^{1 / 2} = T_{2} {(2 V)}^{1 / 2} \Rightarrow T_{2} = \frac{T}{\sqrt{2}}$

$W = \frac{R (T_{1} - T_{2})}{γ - 1} = \frac{R (T - \frac{T}{\sqrt{2}})}{1 / 2} = R T (2 - \sqrt{2})$

Solution

Q.
A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is $(given, γ = \frac{3}{2})$ [2023]

1 $W = T R [\sqrt{2} - 2]$

2 $W = \frac{T}{R} [\sqrt{2} - 2]$

3 $W = \frac{R}{T} [2 - \sqrt{2}]$

4 $W = T R [2 - \sqrt{2}]$

Ans.
(4)

$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$

$T V^{1 / 2} = T_{2} {(2 V)}^{1 / 2} \Rightarrow T_{2} = \frac{T}{\sqrt{2}}$

$W = \frac{R (T_{1} - T_{2})}{γ - 1} = \frac{R (T - \frac{T}{\sqrt{2}})}{1 / 2} = R T (2 - \sqrt{2})$

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Solution

Q. A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is (given, γ=32) [2023]

1 W=TR[2-2]

2 W=TR[2-2]

3 W=RT[2-2]

4 W=TR[2-2]

Ans. (4) T1V1γ-1=T2V2γ-1 TV1/2=T2(2V)1/2⇒T2=T2 W=R(T1-T2)γ-1=R(T-T2)1/2=RT(2-2)

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Q.
A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is $(given, γ = \frac{3}{2})$ [2023]

1 $W = T R [\sqrt{2} - 2]$

2 $W = \frac{T}{R} [\sqrt{2} - 2]$

3 $W = \frac{R}{T} [2 - \sqrt{2}]$

4 $W = T R [2 - \sqrt{2}]$

Ans.
(4)

$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$

$T V^{1 / 2} = T_{2} {(2 V)}^{1 / 2} \Rightarrow T_{2} = \frac{T}{\sqrt{2}}$

$W = \frac{R (T_{1} - T_{2})}{γ - 1} = \frac{R (T - \frac{T}{\sqrt{2}})}{1 / 2} = R T (2 - \sqrt{2})$