Predict the sign of $q, w, Δ U$ of $Δ H$ for given processes
S. NO. Process q w $Δ U$ $ΔH$
1 Melting of solid benzene at 1 atm and normal melting point.
2 Melting of ice at 1 atm and 0°C
3 Adiabatic expansion of one mole of ideal gas.
4 Adiabatic expansion of ideal gas into vacuum.

5 Isothermal expansion of an ideal gas.

6 Heating of perfect gas at constant P.
7 Cooling of perfect gas at constant volume.
Hence, find number of processes for which at least one of q, w, $Δ U$ , $ΔH$ are zero,

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answer is 4.

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Detailed Solution

Signs for each process is given below,

S. NO.	Process	q	w	$Δ U$	$ΔH$
1	Melting of solid benzene at 1 atm and normal melting point.	>0	<0	>0	>0
2	Melting of ice at 1 atm and 0°C	>0	>0	>0	>0
3	Adiabatic expansion of one mole of ideal gas.	0	<0	<0	<0
4	Adiabatic expansion of ideal gas into vacuum.	0	0	0	0
5	Isothermal expansion of an ideal gas.	>0	<0	0	0
6	Heating of perfect gas at constant P.	>0	<0	>0	>0
7	Cooling of perfect gas at constant volume.	<0	0	<0	<0