A cylinder of fixed capacity44.8liters contains helium gas at standered temperature and pressure. What is tge amount of heat needed to raise the temperature of the gas in the cylinder by 15°C
To calculate the amount of heat needed to raise the temperature of the gas in the cylinder, we need to use the formula for heat transfer:
Q = mcΔT
Where:
Q = amount of heat transferred (in joules)
m = mass of the gas (in kilograms)
c = specific heat capacity of the gas (in joules per kilogram per degree Celsius)
ΔT = change in temperature (in degrees Celsius)
First, let's find the mass of the helium gas in the cylinder. To do this, we need to convert the volume of the cylinder to mass using the density of helium gas.
The density of helium gas at standard temperature and pressure (STP) is approximately 0.1786 kg/m^3.
To convert the volume of the cylinder to mass, we need to know the volume of the cylinder. The volume is given as 44.8 liters. However, we need to convert this to cubic meters since the density of helium is given in kg/m^3.
1 liter = 0.001 cubic meters
Therefore, the volume of the cylinder is:
V = 44.8 liters x 0.001 cubic meters/liter = 0.0448 cubic meters
Now, let's calculate the mass of the helium gas:
mass = density x volume = 0.1786 kg/m^3 x 0.0448 cubic meters
Next, we need to find the specific heat capacity of helium. The specific heat capacity of helium at constant pressure (Cp) is approximately 5.193 J/(g·°C). Since the mass is given in kilograms, we need to convert it to grams:
1 kg = 1000 grams
Now, we can calculate the amount of heat:
Q = mass x specific heat capacity x ΔT
Substitute the known values:
Q = (mass in grams) x (specific heat capacity in J/(g·°C)) x ΔT
Finally, plug in the values and calculate:
Q = (mass x 1000) x 5.193 x 15
This will give you the amount of heat needed to raise the temperature of the gas in the cylinder by 15°C.