Answer: To calculate the mass of the helium sample, we can use the ideal gas law equation, which relates the pressure, volume, temperature, and amount of gas for an ideal gas:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = amount of gas in moles
R = universal gas constant
T = temperature in Kelvin
Given information:
Pressure (P) = constant pressure during the process
Initial temperature (T1) = 283 K
Final temperature (T2) = 393 K
Work done by the gas (W) = 40 J
Universal gas constant (R) = 8.31451 J/mol · K
Since the pressure is constant, we can rearrange the ideal gas law equation to solve for the amount of gas (n) in moles:
n = (PV) / (RT)
Substituting the given values into the equation:
n = (constant pressure during the process * volume) / (universal gas constant * temperature)
Now we can calculate the amount of gas in moles.
Next, we can convert the amount of gas from moles to grams using the molar mass of helium (He), which is approximately 4 g/mol.
Finally, we can multiply the mass in grams by 1000 to convert it to grams.
Let's plug in the numbers and do the calculations:
P = constant pressure during the process
V = volume of the gas (not given in the question, need additional information)
R = universal gas constant = 8.31451 J/mol · K
T1 = initial temperature = 283 K
T2 = final temperature = 393 K
W = work done by the gas = 40 J
Molar mass of helium (He) = 4 g/mol
Please provide the value for the volume (V) of the helium gas in order to complete the calculation.