5. The isothermal expansion of 2 kg of air increased its volume by a factor of 1.7 Find the work and the amount of heat supplied, if the temperature of the air is t=70^circ C

To solve this problem, we need to use the first law of thermodynamics and the ideal gas law.<br /><br />Given information:<br />- Mass of air: 2 kg<br />- Volume increase factor: 1.7<br />- Temperature: 70°C<br /><br />Step 1: Calculate the initial volume of the air.<br />Let the initial volume be V1.<br />Since the volume increased by a factor of 1.7, the final volume V2 = 1.7 × V1.<br /><br />Step 2: Calculate the change in volume.<br />ΔV = V2 - V1 = 1.7 × V1 - V1 = 0.7 × V1<br /><br />Step 3: Calculate the work done by the air during isothermal expansion.<br />Work done (W) = nRT ln(V2/V1)<br />Where:<br />n = number of moles of air<br />R = specific gas constant for air<br />T = absolute temperature in Kelvin<br />ln = natural logarithm<br /><br />Step 4: Calculate the amount of heat supplied to the air.<br />Using the first law of thermodynamics:<br />Q = ΔU + W<br />Where:<br />Q = heat supplied<br />ΔU = change in internal energy<br /><br />Since the process is isothermal, ΔU = 0.<br />Therefore, Q = W<br /><br />Therefore, the work done by the air during isothermal expansion is W, and the amount of heat supplied to the air is also W.