A chemical exothermic reaction, that produces Q = 51.24 J of heat, forces a gas,

Question

A chemical exothermic reaction, that produces Q = 51.24 J of heat, forces a gas, with an initial volume V1 = 0.84 Liter, to expand at constant atmospheric pressure, inside a sealed cylinder against a movable piston to a final volume V2 = 0.98 Liter. Calculate the change in internal energy U of the gas in Joules.

       37.1
       -0.1
       75.6
       61.8

n moles of gaseous nitrogen are cooled off from a Temperature T=330 K to just below its liquid temperature of 77 K with a specific enthalpy change H1 = -1490 cal/mol. This amount of nitrogen can be liquefied by extracting some extra heat. The specific heat of vaporization of liquid nitrogen equals H2 = 1336 cal/mol. Calculate the total amount of heat to be extracted from n=0.8 moles of gaseous nitrogen in this process.

       -1068.8
       -2260.8
       -1192
       -1260.8

Please explain

Explanation / Answer

1. H = E + PV

Where , H = heat given to the gas = 51.24 J

E = internal energy change in the gas

PV = work done by the gas

P = pressure , 1 atm

V = 0.98 - 0.84 = 0.14 litre

E = H - PV

= 51.24J - 1atm× 0.14litre = 37.1 J

2. The specific heat of vapourization is 1336 cal/ mol

for 0.8 mole it will be 0.8 ×1336 = 1068.68 cal

Heat released by cooling = - 1490 cal / mol

For 0.8 mol it will be 0.8× -1490 = -1192 cal

The total amount of heat to be extracted = -1068.8 - 1192 = -2260.8cal

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