An ideal diatomic gas occupies a volume V 1 at a pressure P 1 . The gas undergoes a process in which the pressure is proportional to the volume. If at the end of the process the R.M.S. speed of the gas molecules has doubled its initial value, then the heat supplied to the gas, in the given process, is

Question

An ideal diatomic gas occupies a volume V 1 at a pressure P 1 . The gas undergoes a process in which the pressure is proportional to the volume. If at the end of the process the R.M.S. speed of the gas molecules has doubled its initial value, then the heat supplied to the gas, in the given process, is, 7 P 1 V 1, 8 P 1 V 1, 9 P 1 V 1, 10 P 1 V 1

MARKS App · Accepted Answer

As P ∝ V , P V - 1 = constant comparing the above equation with P V x = constant , we get x = - 1 Also, C = C V - R x - 1 = 5 2 R - R - 1 - 1 = 3 R But as RMS speed is doubled therefore temperature becomes four times. Hence, Q = n C Δ T = n × 3 R × 3 T i = 9 n R T i = 9 P 1 V 1

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