Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are labelled as A→ B , A→ C and A → D The change in internal energies during these process are taken as E AB , E AC and E AD and the workdone as W AB W AC and W AD The correct relation between these parameters are:

Question

(A) E AB = E AC = E AD , W AB > 0, W AC =0, W AD > 0 (B) E AB < E AC < E AD , W AB >0, W AC > W AD (C) E AB = E AC < E AD , W AB > 0, W AC =0, W AD < 0 (D) E AB > E AC > E AD , W AB < W AC < W AD

Tardigrade Admin · Accepted Answer

Δ U = nC v Δ T = same AB → volume is increasing ⇒ W > 0 AD → volume is decreasing ⇒ W < 0 AC→ volume is constant ⇒ W =0

$E_{A B} = E_{A C} = E_{A D}, W_{A B} > 0, W_{A C} = 0, W_{A D} > 0$

$E_{A B} < E_{A C} < E_{A D}, W_{A B} > 0, W_{A C} > W_{A D}$

$E_{A B} = E_{A C} < E_{A D}, W_{A B} > 0, W_{A C} = 0, W_{A D} < 0$

$E_{A B} > E_{A C} > E_{A D}, W_{A B} < W_{A C} < W_{A D}$

$Δ U = n C_{v} Δ T =$ same
$A B \to$ volume is increasing $\Rightarrow W > 0$
$A D \to$ volume is decreasing $\Rightarrow W < 0$
$A C \to$ volume is constant $\Rightarrow W = 0$

EAB​=EAC​=EAD​,WAB​>0,WAC​=0,WAD​>0

EAB​<EAC​<EAD​,WAB​>0,WAC​>WAD​

EAB​=EAC​<EAD​,WAB​>0,WAC​=0,WAD​<0

EAB​>EAC​>EAD​,WAB​<WAC​<WAD​

ΔU=nCv​ΔT= same AB→ volume is increasing ⇒W>0 AD→ volume is decreasing ⇒W<0 AC→ volume is constant ⇒W=0

$E_{A B} = E_{A C} = E_{A D}, W_{A B} > 0, W_{A C} = 0, W_{A D} > 0$

$E_{A B} < E_{A C} < E_{A D}, W_{A B} > 0, W_{A C} > W_{A D}$

$E_{A B} = E_{A C} < E_{A D}, W_{A B} > 0, W_{A C} = 0, W_{A D} < 0$

$E_{A B} > E_{A C} > E_{A D}, W_{A B} < W_{A C} < W_{A D}$

$Δ U = n C_{v} Δ T =$ same
$A B \to$ volume is increasing $\Rightarrow W > 0$
$A D \to$ volume is decreasing $\Rightarrow W < 0$
$A C \to$ volume is constant $\Rightarrow W = 0$