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Q.

'n' moles of an ideal monoatomic gas undergo a process in which the temperature changes with volume as $T = {KV}^{2}$ where K is a constant. If the temperature of the gas changes from $T_{0} to 4 T$ then

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a

heat supplied to the gas is $\frac{3}{2} {nRT}_{0}$

b

work done by the gas is $3 nRT$

c

work done by the gas is $\frac{3}{2} {nRT}_{0}$

d

heat supplied to the gas is $6 {nRT}_{0}$

answer is B, C.

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Detailed Solution

$T = {KV}^{2}$

Hence $W = \int P d v = \int_{\sqrt{T_{0} / k}}^{2 \sqrt{T_{0} / k}} n k R v d v = \frac{3 n R T_{0}}{2}$

$\begin{array}{l} Δu = {nC}_{v} ΔT = \frac{n 3 R}{2} \cdot 3 T_{0} = \frac{9 nRT}{2} \\ ∴ ΔQ = Δu + ΔW = 6 {nRT}_{0} \end{array}$

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