The pressure in a constant-volume gas thermometer is 0.700atm at 100 deg. Celsius and 0.512atm at 0 deg. Celsius.
a) What is the temperature when the pressure is 0.0550atm?
b)What is the pressure at 500 deg. Celsius?
a) To find the temperature when the pressure is 0.0550atm, we can use the relationship between pressure and temperature in a constant-volume gas thermometer, which is described by Gay-Lussac's Law:
P1/T1 = P2/T2
where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
We are given the following values:
P1 = 0.700atm
T1 = 100°C = 373K
P2 = 0.0550atm
Let's substitute the values into the equation and solve for T2:
0.700atm / 373K = 0.0550atm / T2
Cross-multiplying and rearranging the equation:
0.700atm x T2 = 373K x 0.0550atm
T2 = (373K x 0.0550atm) / 0.700atm
T2 = 29.59K
Therefore, the temperature when the pressure is 0.0550atm is approximately 29.59K.
b) To find the pressure at 500°C, we can again use Gay-Lussac's Law:
P1/T1 = P2/T2
We are given the following values:
P1 = 0.512atm
T1 = 0°C = 273K
T2 = 500°C = 773K
Let's substitute the values into the equation and solve for P2:
0.512atm / 273K = P2 / 773K
Cross-multiplying and rearranging the equation:
0.512atm x 773K = 273K x P2
P2 = (0.512atm x 773K) / 273K
P2 ≈ 1.447atm
Therefore, the pressure at 500°C is approximately 1.447atm.
To solve these problems, we'll use the relationship between temperature and pressure of a gas in a constant-volume gas thermometer, known as Charles's Law:
\[ \frac{{P_1}}{{T_1}} = \frac{{P_2}}{{T_2}} \]
Where \(P_1\) and \(T_1\) are the initial pressure and temperature, and \(P_2\) and \(T_2\) are the final pressure and temperature.
a) To find the temperature when the pressure is 0.0550 atm, we'll use the given information:
\(P_1 = 0.700\) atm (pressure at 100 °C)
\(T_1 = 100\) °C
\(P_2 = 0.0550\) atm (the desired pressure)
\(T_2 = ?\) (the unknown temperature)
Plugging the known values into Charles's Law, we get:
\[ \frac{{0.700}}{{100}} = \frac{{0.0550}}{{T_2}} \]
Now, let's solve for \(T_2\):
\[ T_2 = \frac{{0.0550}}{{0.700}} \times 100 \]
Calculating this, we find:
\[ T_2 = 7.86 \, \text{°C} \]
Therefore, the temperature when the pressure is 0.0550 atm is approximately 7.86 °C.
b) To find the pressure at 500 °C, we'll use the given information again:
\(P_1 = 0.512\) atm (pressure at 0 °C)
\(T_1 = 0\) °C
\(P_2 = ?\) (the unknown pressure)
\(T_2 = 500\) °C (the desired temperature)
Plugging the known values into Charles's Law, we get:
\[ \frac{{0.512}}{{0}} = \frac{{P_2}}{{500}} \]
Now, let's solve for \(P_2\):
\[ P_2 = \frac{{0.512}}{{0}} \times 500 \]
Calculating this, we find that \(P_2\) is undefined because we have a division by zero.
Therefore, we cannot determine the pressure at 500 °C using the given information.