At a certain absolute temperature T, an ideal diatomic gas has total energy U. Energy E is supplied to the gas and its temperature increases by t on Kelvin scale. If an additional energy E is supplied to the gas, find the final temperature of the gas on Kelvin scale.

Question

At a certain absolute temperature T, an ideal diatomic gas has total energy U.  Energy E is supplied to the gas and its temperature increases by t on Kelvin scale. If  an additional energy E is supplied to the gas, find the final temperature of the gas  on Kelvin scale.

Infinity Learn · Accepted Answer

$$U=5nRT2$$   .....(1)U+E=5nR(T+t)2=5nRT2+5nRt2$$   ......$$(2)⇒$$E=5nRt2$$   ......(3)U+2E=5nRT+t+t$$′$$2=5nR(T+t)2+5nRt$$′$$2=U+E+5nRt$$′$$2$$   ......$$(4)⇒$$E=5nRt$$′$$2$$   ....(5)From$$ $$(3) and (5),t'$$=tHence$$, final temperature of the gas is $$T+t+t$$'$$=T+2t$$ .

At a certain absolute temperature T, an ideal diatomic gas has total energy U. Energy E is supplied to the gas and its temperature increases by t on Kelvin scale. If an additional energy E is supplied to the gas, find the final temperature of the gas on Kelvin scale.

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