550 J of work must be done to compress a gas to half its initial volume at constant temperature. How much work must be done to compress the gas by a factor of 11.0, starting from its initial volume?

The amount of work that must be done to compress the gas 11 times less than its initial pressure is 909.091 J

Explanation:

The given variables are

Work done = 550 J

Volume change = V₂ - V₁ = - 0.5V₁

Thus the product of pressure and volume change = work done by gas, thus

P * - 0.5V₁ = 500 J

Hence - PV₁ = 1000 J

also P₁/V₁ = P₂/V₂ but V₂ = 0.5V₁ Therefore P₁/V₁ = P₂/0.5V₁ or P₁ = 2P₂

Also to compress the gas by a factor of 11 we have

P (V₂ - V₁) = P * (V₁/11 - V₁) = P (11V₁ - V₁) / 11 = P*-10V₁/11 = - PV₁*10/11 = 1000 J * 10/11 = 909.091 J of work