A diatomic gas, having CP=72R and CV=52R, is heated at constant pressure. The ratio dU:dQ:dW is

dU=nCvdT=n52RdTdQ=nCpdT=n72RdTdW=nRdT Thus, dU:dQ:dW=n52RdT:n72RdT:nRdT=52:72:1=5:7:2

A diatomic gas, having CP=72R and CV=52R, is heated at constant pressure. The ratio dU:dQ:dW is

dU=nCvdT=n52RdTdQ=nCpdT=n72RdTdW=nRdT Thus, dU:dQ:dW=n52RdT:n72RdT:nRdT=52:72:1=5:7:2

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A diatomic gas, having $C_{P} = \frac{7}{2} R$ and $C_{V} = \frac{5}{2} R$ , is heated at constant pressure. The ratio $d U : d Q : d W i s$

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5:7:2

5:7:3

3:5:2

3:7:2

answer is A.

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Detailed Solution

$\begin{array}{l} d U = n C_{v} d T = n (\frac{5}{2}) R d T \\ d Q = n C_{p} d T = n (\frac{7}{2}) R d T \\ d W = n R d T \\ Thus, d U : d Q : d W = n (\frac{5}{2}) R d T : n (\frac{7}{2}) R d T : n R d T \\ = \frac{5}{2} : \frac{7}{2} : 1 \\ = 5 : 7 : 2 \end{array}$