When a small amount of heat Δ Q is added to an enclosed gas, then increase in internal energy and external work done are related as

Question

When a small amount of heat Δ Q is added to an enclosed gas, then increase in internal energy and external work done are related as (A) m CV Δ T=Δ Q+p Δ V (B) Δ Q=m CV Δ T+p Δ V (C) m CV=Δ Q+p Δ V (D) Δ Q=m Cp Δ T+p Δ V

Tardigrade Admin · Accepted Answer

As , Δ Q=Δ U+Δ W=m CV(Δ T)+p(Δ V)

Q. When a small amount of heat $Δ Q$ is added to an enclosed gas, then increase in internal energy and external work done are related as

$m C_{V} Δ T = Δ Q + p Δ V$

$Δ Q = m C_{V} Δ T + p Δ V$

$m C_{V} = Δ Q + p Δ V$

$Δ Q = m C_{p} Δ T + p Δ V$

$A s, Δ Q = Δ U + Δ W = m C_{V} (Δ T) + p (Δ V)$

Q. When a small amount of heat ΔQ is added to an enclosed gas, then increase in internal energy and external work done are related as

mCV​ΔT=ΔQ+pΔV

ΔQ=mCV​ΔT+pΔV

mCV​=ΔQ+pΔV

ΔQ=mCp​ΔT+pΔV

As,ΔQ=ΔU+ΔW=mCV​(ΔT)+p(ΔV)