A gas is compressed from a volume of 2 m3 to a volume of 1 m3 at a constant pressure of 100 N/m2. Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas :

Question

A gas is compressed from a volume of 2 m3 to a volume of 1 m3 at a constant pressure of 100 N/m2. Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas : (A) Increases by 250 J (B) Decreases by 250 J (C) Increases by 50 J (D) Decreases by 50 J

Tardigrade Admin · Accepted Answer

As we know, Δ Q = Δ u+Δ w (Ist law of thermodynamics) ⇒ Δ Q = Δ u+PΔ v or 150 = Δ u+100(1-2) = Δ u-100 ∴ Δ u = 150+100 = 250J Thus the internal energy of the gas increases by 250 J

Q. A gas is compressed from a volume of $2 m^{3}$ to a volume of $1 m^{3}$ at a constant pressure of $100 N / m^{2}$ . Then it is heated at constant volume by supplying $150 J$ of energy. As a result, the internal energy of the gas :

Increases by 250 J

Decreases by 250 J

Increases by 50 J

Decreases by 50 J

As we know,
$Δ Q = Δ u + Δ w$
( $I^{s t}$ law of thermodynamics)
$\Rightarrow Δ Q = Δ u + P Δ v$
or $150 = Δ u + 100 (1 - 2)$
$= Δ u - 100$
$∴ Δ u = 150 + 100 = 250 J$
Thus the internal energy of the gas increases by $250 J$

Q. A gas is compressed from a volume of 2m3 to a volume of 1m3 at a constant pressure of 100N/m2. Then it is heated at constant volume by supplying 150J of energy. As a result, the internal energy of the gas :