One mole of an ideal monatomic gas is taken through a thermodynamic process shown in the P-V diagram. The heat supplied to the system in this process is K×(180/2+10)P0V0. Determine the value of K.

To determine the value of K, we need to analyze the given expression for the heat supplied to the system in the thermodynamic process. The expression is K×(180/2+10)P0V0.

Let's simplify the expression step by step:

1. Simplify the expression inside the parentheses: 180/2+10 = 90+10 = 100.

2. Now we have K×100P0V0.

3. Since we are given that the gas is an ideal monatomic gas, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

4. In this case, we are given that we have one mole of the gas, so n = 1.

5. Rearranging the ideal gas law, we have PV = RT.

6. Dividing both sides of the equation by V, we get P = (RT)/V.

7. Substituting this expression for P into our original expression, we have K×100((RT)/V)0V0.

8. Simplifying further, we have K×100RT.

9. Now, we know that heat supplied to the system is given by the equation Q = nCΔT, where Q is the heat, n is the number of moles, C is the molar heat capacity, and ΔT is the change in temperature.

10. In this case, we are given that the heat supplied is K×100RT.

11. Since we have one mole of the gas, n = 1, and we can rewrite the equation as Q = CΔT.

12. Comparing this equation with our given expression, we can equate the two: K×100RT = CΔT.

13. From this equation, we can see that K = CΔT/(100RT).

Therefore, the value of K is CΔT/(100RT).