Question

1 mole of an ideal gas A (C v,m = 3R) and 2 mole of an ideal gas B are $\left( C_{v,m} = \frac{3}{2}R \right)$ taken in a container and expanded reversible and adiabatically from 1 litre to 4 litre starting from initial temperature of 320 K. $\Delta$E or $\Delta$U for the process is :

• A. –240 R
• B. –240 R
• C. 480 R
• D. –960 R

Answer 1

Answer: (D)

–960 R

Answer 2

Avg. CV, m = $\frac{n_{1}C_{v,m} + n_{2}C_{v,m_{2}}}{n_{1} + n_{2}}$

= $\frac{1 \times 3R + 2 \times \frac{3}{2}R}{3}$ =2R

T1V1g–1 = T2V2g–1 $\Rightarrow$ 320 × $1^{\frac{3}{2} - 1}$ = T2 ×(4)3/2–1

$\Rightarrow$ T2 =160 K

$\Delta$U = (n1 + n2) CV,avg $\Delta$T

= 3 × 2R × (160 – 320) = –960 R