Two adiabatic cylinders A and B, fitted with insulated 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 slowly to the gas in each cylinder. If the rise in temperature of the gas in cylinder A is 30 K, then rise in temperature of the gas in cylinder B is 7 × x kelvin. Value of x is:
Physics · Mixed Chapter
JEE Mains

Question

Two adiabatic cylinders A and B, fitted with insulated 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 slowly to the gas in each cylinder. If the rise in temperature of the gas in cylinder A is 30 K, then rise in temperature of the gas in cylinder B is 7 × x kelvin. Value of x is:

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Although the cylinders are thermally insulating, the problem states that equal heat is supplied; gas A expands at approximately constant pressure, while gas B has fixed volume. Step 2: For a diatomic ideal gas, C_P=(7/2)R and C_V=(5/2)R. Step 3: Equal supplied heat gives nC_P×30=nC_V×ΔT_B, so ΔT_B=(7/5)×30=42 K. Step 4: Since ΔT_B=7x K, x=42/7=6.