The heat supplied to a gas at a constant pres | vedclass

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Question

(A) According to the First Law of Thermodynamics,$Q = \Delta U + W$,where $Q$ is the heat supplied,$\Delta U$ is the change in internal energy,and $W$

Vedclass · Accepted Answer

$250$

Vedclass · Answer

(A) According to the First Law of Thermodynamics,$Q = \Delta U + W$,where $Q$ is the heat supplied,$\Delta U$ is the change in internal energy,and $W$ is the work done by the gas.Given: Heat supplied $Q = 1000 \ kJ = 10^6 \ J$.Pressure $P = 5 	imes 10^5 \ Pa$.Initial volume $V_1 = 1 \ m^3$,Final volume $V_2 = 2.5 \ m^3$.Work done at constant pressure is given by $W = P(V_2 - V_1)$.$W = 5 	imes 10^5 	imes (2.5 - 1) = 5 	imes 10^5 	imes 1.5 = 7.5 	imes 10^5 \ J = 750 \ kJ$.Now,substituting the values into the First Law equation:$1000 \ kJ = \Delta U + 750 \ kJ$.$\Delta U = 1000 \ kJ - 750 \ kJ = 250 \ kJ$.Therefore,the change in internal energy is $250 \ kJ$.

The heat supplied to a gas at a constant pressure of $5 \times 10^5 \ Pa$ is $1000 \ kJ$. If the volume of gas changes from $1 \ m^3$ to $2.5 \ m^3$,then the change in internal energy of the gas is (in $kJ$)

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