Two moles of an ideal monoatomic gas at an initial temperature T₀ are suddenly compressed such that its pressure becomes 32 times its initial pressure. The magnitude of work done on the gas during this process is:

Step-by-step solution

The phrase "suddenly compressed" indicates that the process is adiabatic. For an ideal monoatomic gas, the ratio of specific heats is = 5 3 and the molar heat capacity at constant volume is C_v = 3 2 R . The relation between temperature and pressure in an adiabatic process is: T P^ -1 Calculating the exponent: -1 = 5 3 -1 5 3 = 2 5 Given that P₂ = 32P₁ , we can find the final temperature T₂ : T₂ = T₀ ( 32P₁ P₁ )^ 2 5 = T₀ (32)^ 2 5 = T₀ (2^5)^ 2 5 = 4T₀ The change in temperature is T = T₂ - T₀ = 4T₀ - T₀ = 3T₀ . Fr