A sample of gas is compressed at a pressure, of 0.5 atm from a volume of $400 {c m}^{3}$ to $200 {c m}^{3}$ . During the process to 8.0 J of heat flows to the surrounding. Calculate the change in the internal energy of the system.

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Solution

Given: $Q = - 8 J, V_{1} = 400 c m^{2} = 0.4 L$
$V_{2} = 200 c m^{3} = 0.2 L$
$W o r k = - P_{e x t} (V_{2} - V_{1})$
$W = - 0.5 a t m (0.2 - 0.4) L$
$W = 0.5 \times 0.2 L - a t m = 0.1 L - a t m$
$W = 0.1 \times 101.33 J o u l e$
$W = 10.13 J$ $[1 L - a t m = 101.33 J]$
From first law of thermodynamics,
$△ U = Q + W$
$△ U = - 8 J + 10.13 J$
$△ U = 2.13 J$

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A sample of gas is compressed at a pressure, of 0.5 atm from a volume of 400cm3 to 200cm3. During the process to 8.0 J of heat flows to the surrounding. Calculate the change in the internal energy of the system.

Given: Q=−8 J, V1=400 cm2=0.4LV2=200 cm3=0.2 LWork=−Pext(V2−V1)W=−0.5 atm(0.2−0.4)LW=0.5×0.2 L−atm=0.1 L−atmW=0.1×101.33 JouleW=10.13 J [1 L−atm=101.33 J]From first law of thermodynamics, △U=Q+W△U=−8 J+10.13 J△U=2.13 J

A sample of gas is compressed at a pressure, of 0.5 atm from a volume of $400 {c m}^{3}$ to $200 {c m}^{3}$ . During the process to 8.0 J of heat flows to the surrounding. Calculate the change in the internal energy of the system.