There is gas in a gas container. A valve on the container will be opened and a quarter of the gas quantity will be released to the outer range. Due to this process the temperature of the gas will be decreased by 20%. What is the decrease of the gas pressure?
p1v1=nRT
P2V2=.75nRt2
V1=V2
P2=.75nRT2P1/nRT1
but T2=.8T1
P2/P1=.75*.8=.6
soPressure 2 is sixty percent of the original pressure.
check my work
To determine the decrease in gas pressure, we need to understand the relationship between gas temperature and pressure. According to the ideal gas law, the relationship between pressure (P), volume (V), and temperature (T) of a gas is given by the formula: PV = nRT, where n is the number of moles of gas and R is the ideal gas constant.
In this case, we are only concerned with the change in temperature and pressure. The other variables such as volume and moles of gas remain constant.
Let's assume the initial pressure of the gas in the container is P1, and the decrease in temperature due to releasing a quarter of the gas is T1.
1. Calculate the new temperature after the decrease:
T2 = T1 - 20% * T1
2. Calculate the ratio of initial and final temperatures:
T_ratio = T2 / T1
3. Since the volume and moles of gas are constant, we can assume that the ratio of pressures is the same as the ratio of temperatures:
P_ratio = T_ratio
4. Calculate the decrease in pressure:
P_decrease = (1 - P_ratio) * P1
Therefore, the decrease in gas pressure is P_decrease.
To determine the decrease in gas pressure, we need to understand the relationship between gas pressure and temperature. According to the ideal gas law, the pressure of a gas is directly proportional to its temperature when the volume is constant.
Given that the gas quantity decreases by a quarter and the temperature decreases by 20%, we can calculate the decrease in gas pressure by following these steps:
1. Assume the initial gas pressure is P.
2. As the gas quantity decreases by a quarter, the remaining gas quantity will be 3/4 of the original quantity.
3. The temperature decreases by 20%, which means the final temperature will be 80% of the initial temperature.
4. According to the ideal gas law, the equation can be written as:
P1 / T1 = P2 / T2
where P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure, and T2 is the final temperature.
5. Substituting the given values:
P / 1 = (3/4)P2 / (0.8T)
6. Cross-multiplying and simplifying:
0.8P = (3/4)P2
7. Solving for P2:
P2 = (4/3) * 0.8P
= (32/30)P
= (16/15)P
8. The decrease in gas pressure can be calculated by finding the difference between the initial and final pressure:
Decrease in gas pressure = Initial pressure - Final pressure
= P - (16/15)P
= (15/15)P - (16/15)P
= (1/15)P
Therefore, the decrease in gas pressure is (1/15) of the initial gas pressure.