For an ideal gas undergoing an adiabatic process, a graph is plotted between P (on the y -axis) and T (on the x -axis), where P is the pressure and T is the absolute temperature of the gas. If the graph is a straight line with a slope of 5 2 , the ratio of specific heats ( C_p C_v ) for the gas is:

Step-by-step solution

For an adiabatic process, the relationship between pressure P and temperature T is given by: T^ P^ 1- = constant Taking the natural logarithm on both sides: T + (1- ) P = C Rearranging to the form of a straight line equation ( y = mx + c ): P = ( -1 ) T + C' The slope of the graph is m = -1 . Given that the slope is 5 2 : -1 = 5 2 2 = 5 - 5 3 = 5 = 5 3 Answer: 5 3