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Manipal Medical Manipal Medical Solved Paper-2004

  • question_answer
    Two cylinders fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of gas in A is 300 K, then rise in temperature of gas in B is:

    A)  30 K

    B)  18 K

    C)  50 K

    D)  42 K

    Correct Answer: D

    Solution :

     In cylinder A heat is supplied at constant pressure while in cylinder B heat is supplied at constant volume. \[\therefore \] \[{{(\Delta Q)}_{A}}=n{{C}_{p}}{{(\Delta T)}_{A}}\]        ...(1) and   \[{{(\Delta Q)}_{B}}=n{{C}_{V}}{{(\Delta T)}_{B}}\]        ...(2) Given: \[{{(\Delta Q)}_{A}}={{(\Delta Q)}_{B}}\] \[\therefore \] \[{{(\Delta T)}_{B}}=\frac{{{C}_{P}}}{{{C}_{V}}}{{(\Delta T)}_{A}}\] \[=1.4\times 30\] \[\left( \because \frac{{{C}_{P}}}{{{C}_{V}}}=1.4 \right)\] \[=42\,K\]


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