# Thermodynamics - Question with my answer

A gas is compressed from an initial volume of 5.40 L to a final volume of 1.23 L by an external pressure of 1.00 atm . During the compression the gas releases 128 J of heat.

given data :
v1 = 5.40 l
v2 = 1.23 l
P1 - 1.00

now convert L to m^3 and atm to pa so
1 l =0.001 cubic meters
1 atm = 101,325 pa
v1 = 5.4X10^-3 m^3
v2 = 1.23 X 10^-3 m^3
p = 101325 pa

now DU = -Q - W
w = -pXDv = 101325(1.23 X 10^-3 - 5.4X10^-3 )
w = 422.5 J

now DU = -Q + W
= -128 + 422.5
Du = 294.5 J

W = p ΔV
= - 423 J
The negative work being done means that it is receiving energy from an external source (doing work on it)
Q = -128 J
The negative means that it is losing energy (heat)
so that from
ΔU = Q - W
= -128 -(-423)
= 295 J
the internal energy increased by this amount

thanks, but how we can no from the question that the system receiving energy from an external source ...?

Work and energy go hand in hand. The system will loose energy if it is doing positive work and gain energy if it is doing negative work. It is doing positive work if it is expanding, since it is exerting an outwards force against the atmosphere while expanding, negative work if contracting, since the system is still exerting an outwards force on the atmosphere, but now it is motioning in the opposite direction to the force, that is contracting inwards. Also if ΔU is positive then we have a net energy flow into the system. We also need to consider the heat flow, which is a form of energy.

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