Advertisements
Advertisements
प्रश्न
70 calories of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from 30° C to 35° C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is
विकल्प
30 calories
50 calories
70 calories
90 calories
Advertisements
उत्तर
50 calories
It is given that 70 calories of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from 30° C to 35° C. Also, specific heat at constant pressure,
`"C"_"P" = (triangle Q)/(ntriangleT)`
`=> "C"_"P" = 70/ (2 xx (35-30)`
`=> "C"_"P" =70/(2 xx 5)`
`=> "C"_"P" = 7 "calories" -" mol" ^-1K^-1`
For an ideal gas ,
CP - CV = R = 8.314 J - mol -1 K-1 ≃ 2 calories mol-1K-1
⇒ CV =CP -R
⇒ CV = (7-2) calories - mol-1 K-1
⇒ CV = 5 calories - mol-1 K-1
⇒ CV = `(triangle "Q")/(ntriangle"T")`
`=> 5 = (triangle "Q")/(2 xx (35-30)`
⇒ Δ Q = 5 × 2 × (35-30)
⇒ Δ Q = 5 × 2 × 5
⇒ Δ Q = 50 calories
Therefore, 50 calories need to be supplied to raise the temperature of 2 moles of gas from 30-35 oC at constant volume.
APPEARS IN
संबंधित प्रश्न
Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3Å.
An air bubble of volume 1.0 cm3 rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35 °C?
The density of an ideal gas is 1.25 × 10−3 g cm−3 at STP. Calculate the molecular weight of the gas.
Use R=8.31J K-1 mol-1
Consider a sample of oxygen at 300 K. Find the average time taken by a molecule to travel a distance equal to the diameter of the earth.
Use R=8.314 JK-1 mol-1
Find the ratio of the mean speed of hydrogen molecules to the mean speed of nitrogen molecules in a sample containing a mixture of the two gases.
Use R = 8.314 JK-1 mol-1
Hydrogen gas is contained in a closed vessel at 1 atm (100 kPa) and 300 K. (a) Calculate the mean speed of the molecules. (b) Suppose the molecules strike the wall with this speed making an average angle of 45° with it. How many molecules strike each square metre of the wall per second?
Use R = 8.31 JK-1 mol-1
A uniform tube closed at one end, contains a pellet of mercury 10 cm long. When the tube is kept vertically with the closed-end upward, the length of the air column trapped is 20 cm. Find the length of the air column trapped when the tube is inverted so that the closed-end goes down. Atmospheric pressure = 75 cm of mercury.
Work done by a sample of an ideal gas in a process A is double the work done in another process B. The temperature rises through the same amount in the two processes. If CAand CB be the molar heat capacities for the two processes,
For a solid with a small expansion coefficient,
The value of Cp − Cv is 1.00 R for a gas sample in state A and 1.08 R in state B. Let pAand pB denote the pressures and TA and TB denote the temperatures of the states A and B, respectively. It is most likely that
Let Cv and Cp denote the molar heat capacities of an ideal gas at constant volume and constant pressure respectively. Which of the following is a universal constant?
The figure shows a process on a gas in which pressure and volume both change. The molar heat capacity for this process is C.
The molar heat capacity for the process shown in the figure is
The molar heat capacity of oxygen gas at STP is nearly 2.5 R. As the temperature is increased, it gradually increases and approaches 3.5 R. The most appropriate reason for this behaviour is that at high temperatures
A sample of an ideal gas (γ = 1.5) is compressed adiabatically from a volume of 150 cm3 to 50 cm3. The initial pressure and the initial temperature are 150 kPa and 300 K. Find (a) the number of moles of the gas in the sample (b) the molar heat capacity at constant volume (c) the final pressure and temperature (d) the work done by the gas in the process and (e) the change in internal energy of the gas.
One mole of gas expands obeying the relation as shown in the P-V diagram. The maximum temperature in this process is equal to ______.
