The temperature of gas of volume 50cm Cube is at 32 degree at pressure of 300mmhg . Calculate the temperature when the volume is 80cm cube at pressure 360mmhg
To calculate the new temperature, we can use the ideal gas law: 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 in Kelvin.
First, calculate the initial number of moles of gas using the initial conditions:
P1 = 300 mmHg = 300/760 atm
V1 = 50 cm^3
T1 = 32 degrees Celsius = 273 + 32 = 305 K
Using the ideal gas law, we can calculate the number of moles at initial conditions:
n = (P1 * V1) / (R * T1)
Now, we need to find the new temperature when the volume is 80 cm^3 and the pressure is 360 mmHg. Let's denote the new temperature as T2.
P2 = 360 mmHg = 360/760 atm
V2 = 80 cm^3
Using the ideal gas law again, we can calculate the new temperature:
T2 = (P2 * V2 * T1) / (P1 * V1)
Plug in the values we have calculated:
T2 = (360/760 * 80 * 305) / (300/760 * 50)
T2 = (0.4737 * 24400) / (0.3947 * 50)
T2 = 20318.8 / 19.74
T2 = 1029 K
Therefore, the temperature of the gas at a volume of 80 cm^3 and a pressure of 360 mmHg is 1029 K.