Question
Derive a relation between temperature and volume for an adiabatic process. of helium gas at temperature of
undergoes reversible adiabatic expansion from an initial volume of
to
. Calculate the final temperature of the gas by assuming that the helium behaves ideally and has
.
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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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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