Two cylinders A and B fitted with pistons contain equal number of moles of an ideal monoatomic gas at 400 ~K . The piston of A is free to move while that of B is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is 42 ~K , the rise in temperature of the gas in B is

Step-by-step solution

From first law of thermodynamics Q= U+W For cylinder A pressure remains constant Work done by a system W= R -1 (T₁-T₂ ) For monoatomic gases aligned & =1 & = 5 3 W & = 1 R 5 3 -1 (442-400) & = 3 2 R 42 aligned or =63 R But U=0 , for cylinder A aligned Q & =0+63 R Q & =63 R aligned For cylinder B volume is constant, aligned W =0 and Q= C_V T aligned For monoatomic gas aligned C_V & = 3 2 R Q & =1 3 2 R T aligned As heat given to both cylinder is same aligned 63 R & = 3 2 R T T & =42 ~K aligned