Question

N moles of an ideal monatomic gas is heated from 35 degree Celsius to 55 degree Celsius at constant volume and 900J of heat is absorbed.If same gas is heated at constant pressure from 55 degree Celsius to 95 degree Celsius,then the heat required will be​

Answer 1

HEAT REQUIRED OR MOLAR HEAT CAPACITY

THE AMOUNT OF HEAT REQUIRED TO INCREASE THE TEMPERATURE OF ONE MOLE OF GAS BY 1°C IS KNOWN AS MOLAR HEAT CAPACITY.

BUT THERE IS TWO TYPE OF MOLAR HEAT CAPACITY.

1. HEAT REQUIRED TO INCREASE THE TEMPERATURE OF ONE MOLE OF GAS BY 1°C AT CONSTANT PRESSURE.(Cp)

2. HEAT REQUIRED TO INCREASE THE TEMPERATURE OF ONE MOLE OF GAS BY 1°C AT CONSTANT VOLUME.(Cv)

NOW YOUR SOLUTION IS GIVEN BELOW

$relation \: between \: these \: two \: heat \: \\ capacities..... \\ \\ \frac{molar \: heat \: capacity(cons. \: Pres.)}{molar \: heat \: capacity(cons. \: vol} = \alpha .......eq(1) \\ \\ where \: \alpha \: has \: diffierent \: value \: depending \\ on \: atomicity \: of \: gas \\ \\ \alpha = 3(mono \: atomic \: gas) \\ \\ as \: u \: see \: temperature \: difference \\ \: in \: both \: cases \: is \: 20 \\ \\ so \: heat \: required \: in \: increasing \: \\ 20 \: celsius \: is..... \\ \\ 20(molar \: heat \: capacity \: at \: const \: volu) = 900 \\ (given) \\ \\ heat \: required \: to \: raise \: temperature \: \\ by \: 20 \: at \: contant \: pressure \\ \\ 20(molar \: heat \: capacity \: cons \: press) = q \\ \\ put \: value \: of \: both \: heat \: capacity \: in \\ eq(1) \\ \\ \frac{ \frac{q}{20} }{ \frac{900}{20} } = 3 \\ \\ \frac{q}{900} = 3 \\ \\ q = 2700joules$