Derive a relation between temperature and volume for an adiabati

Question

Derive a relation between temperature and volume for an adiabatic process. $1.00\text{ mole}$ of helium gas at temperature of $100\text{ }^\circ\text{C}$ undergoes reversible adiabatic expansion from an initial volume of $5\text{ dm}^3$ to $30\text{ dm}^3$ . Calculate the final temperature of the gas by assuming that the helium behaves ideally and has $C_{V,m} = 12.47\text{ JK}^{-1}\text{mol}^{-1}$ .

19 Jan 2026

Answer :

Word Count : 407

Let's solve this **step by step**. ## Step 1: Start with the first law of thermodynamics for an adiabatic process For an **adiabatic process**, there is no heat exchange: [ dQ = 0 ] So, the **first law** becomes: [ dU = -dW ] For an ideal gas: [ dU = n C_V dT ] and [ dW = P,dV ] So: [ n C_V dT = _______ ______ _____ ______ _________.
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