When a definite amount of work is done a certain amount of heat is produced and vice versa.
It can be mathematically expressed as
W = JH
where 'J' is a constant called Mechanical equivalent of heat and 'H' is heat produced.
But a true version of the law is stated as follows
“When an amount of heat is supplied to a system a part of it is used in raising internal energy of the system and a part in doing the work.”
dQ = dU + dW
where
dQ - amount of heat supplied ;
dU - change in internal energy ;
dW - change in work
From the first law it could be inferred that it is impossible to derive any work without expenditure of an equivalent amount of energy in some other forms.
According to first law "The energy of universe remains constant".
For mathematical calculations it should be kept in mind that heat absorbed by the system should be taken as "positive" and rejected by the system should be taken as "negative".
Let us now apply first law to some thermodynamic processes.
i) In an isothermal change dU=0 and dQ = dW; thus in an isothermal change the quantiity of heat absorbed by a perfect gas is transformed into work by the gas.
ii) In an adiabatic process, dQ=0 and dU+dW=0 -> dU = - dW
a) If the system is compressed, work is done on the gas and thus dW is taken as -ve.
Hence dU = -(-dW) = dW
b) If the system expands adiabatically 'dW' is positive.
Hence dU=-(+dW) = -dW
iii) In an adiabatic compression, the decrease in volume is associated with increase in temperature and
increase in pressure.
