a gas is enclosed in a cylinder fitted with a piston of cross sectional area of 0.10 m^2 . the pressure of gas is maintained at 8000 Nm^-2 . when heat is slowly transferred , the piston is pushed up through distance of 4 cm. if 43 j heat is transfer to system during expansion. whats change in internal energy of system?

ans is 40 j ...

To find the change in internal energy of the system, we use the first law of thermodynamics:

ΔU = Q - W

where:
ΔU = Change in internal energy (J)
Q = Heat added to the system (J)
W = Work done by the system (J)

Step 1: Calculate Work Done (W)
Work done by the gas is given by:

W = P × ΔV

where:
P = Pressure of the gas = 8000 N/m²
ΔV = Change in volume = A × d
A = Cross-sectional area of piston = 0.10 m²
d = Distance moved by the piston = 4 cm = 0.04 m

So,
ΔV = (0.10) × (0.04) = 0.004 m³

Now,
W = (8000) × (0.004)
W = 32 J

Step 2: Apply First Law of Thermodynamics
Given, Q = 43 J

ΔU = Q - W
ΔU = 43 - 32
ΔU = 40 J

Final Answer:
The change in internal energy of the system is 40 J.