A frictionless piston-cylinder device and a rigid tank contain 3 kmol of an ideal gas at the same temperature, pressure and volume. now heat is transferred, and the temperature of both systems is raised by 10°c. the amount of extra heat that must be supplied to the gas in the cylinder that is maintained at constant pressure is.

Explanation:

Extra heat can be determine by the work needed in the piston cylinder system.

= PΔV

          = mRΔT

          = ΔT

           = nR*ΔT

∵ R is the gas constant its value is 8.31447 J/mol.K

           = 3×8.31447×10          

           =249.43 KJ

So the extra heat that must be supplied to the gas is 249.43 KJ.

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we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .