Consider a cycle tyre being filled with air by a pump. Let V be the volume of the tyre (fixed) and at each stroke of the pump DeltaV (=V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from P_(1)to P_(2) ?

Consider a cycle tyre being filled with air by a pump. Let V be the vo

1.	Consider a cycle tyre being filled with air by a pump. Let V be the volume of the tyre (fixed) and at each stroke of the pump DeltaV (=V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from P_(1)to P_(2) ?
Answer» SOLUTION :`P(V +Delta UPSILON)^(gamma) = (P+DELTAP)V^(gamma)` `P[1+ gamma (Delta upsilon)/(V)] = P(1+(Delta p)/(P))` `gamma (Delta upsilon)/(V) =(Deltap)/(P), (d upsilon)/(dp) = (V)/(gammaP)` `W.D. = int_(P_(1))^(P_(2)) P d upsilon=int_(P_(1))^(P_(2))"P" (V)/(gammaP) dp = ((P_(2)-P_(1)))/(gamma)V`