Advertisements
Advertisements
प्रश्न
Air is pumped into an automobile tyre's tube up to a pressure of 200 kPa in the morning when the air temperature is 20°C. During the day the temperature rises to 40°C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature.
उत्तर
Here,
\[ P_1 = 2 \times {10}^5 Pa \]
P2 = ?
T1 = 293 K
T2 = 313 K
V2 = V1 + 0.02 V1 = V1 (1.02)
Now,
\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]
\[\Rightarrow \frac{2 \times {10}^5 V_1}{293} = \frac{P_2 V_1 (1.02)}{313} \]
\[ \Rightarrow P_2 = \frac{2 \times {10}^5 \times 313}{293 \times 1.02} = 209 \text{ kPa }\]
APPEARS IN
संबंधित प्रश्न
A gas is kept in a rigid cubical container. If a load of 10 kg is put on the top of the container, does the pressure increase?
If it were possible for a gas in a container to reach the temperature 0 K, its pressure would be zero. Would the molecules not collide with the walls? Would they not transfer momentum to the walls?
A gas behaves more closely as an ideal gas at
2 g of hydrogen is sealed in a vessel of volume 0.02 m3 and is maintained at 300 K. Calculate the pressure in the vessel.
Use R=8.3J K-1 mol-1
Figure shows a cylindrical tube with adiabatic walls and fitted with a diathermic separator. The separator can be slid in the tube by an external mechanism. An ideal gas is injected into the two sides at equal pressures and equal temperatures. The separator remains in equilibrium at the middle. It is now slid to a position where it divides the tube in the ratio of 1:3. Find the ratio of the pressures in the two parts of the vessel.
Use R=8.314J K-1 mol-1
A vessel contains 1.60 g of oxygen and 2.80 g of nitrogen. The temperature is maintained at 300 K and the volume of the vessel is 0.166 m3. Find the pressure of the mixture.
Use R = 8.3 J K-1 mol-1
A container of volume 50 cc contains air (mean molecular weight = 28.8 g) and is open to atmosphere where the pressure is 100 kPa. The container is kept in a bath containing melting ice (0°C). (a) Find the mass of the air in the container when thermal equilibrium is reached. (b) The container is now placed in another bath containing boiling water (100°C). Find the mass of air in the container. (c) The container is now closed and placed in the melting-ice bath. Find the pressure of the air when thermal equilibrium is reached.
Use R = 8.3 J K-1 mol-1
In an adiabatic process on a gas with γ = 1.4, the pressure is increased by 0.5%. The volume decreases by about
A vessel of volume V0 contains an ideal gas at pressure p0 and temperature T. Gas is continuously pumped out of this vessel at a constant volume-rate dV/dt = r keeping the temperature constant. The pressure of the gas being taken out equals the pressure inside the vessel. Find (a) the pressure of the gas as a function of time, (b) the time taken before half the original gas is pumped out.
Use R = 8.3 J K−1 mol−1
An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 and weight 1 kg. The length of the gas column in the vessel is 20 cm. The atmospheric pressure is 100 kPa. The vessel is now taken into a spaceship revolving round the earth as a satellite. The air pressure in the spaceship is maintained at 100 kPa. Find the length of the gas column in the cylinder.
Use R = 8.3 J K-1 mol-1
Two glass bulbs of equal volume are connected by a narrow tube and are filled with a gas at 0°C at a pressure of 76 cm of mercury. One of the bulbs is then placed in melting ice and the other is placed in a water bath maintained at 62°C. What is the new value of the pressure inside the bulbs? The volume of the connecting tube is negligible.
Three samples A, B and C of the same gas (γ = 1.5) have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for A, adiabatic for B and isobaric for C. If the final pressures are equal for the three samples, find the ratio of the initial pressures.
A barometer correctly reads the atmospheric pressure as 76 cm of mercury. Water droplets are slowly introduced into the barometer tube by a dropper. The height of the mercury column first decreases and then becomes constant. If the saturation vapour pressure at the atmospheric temperature is 0.80 cm of mercury, find the height of the mercury column when it reaches its minimum value.
The temperature and humidity of air are 27°C and 50% on a particular day. Calculate the amount of vapour that should be added to 1 cubic metre of air to saturate it. The saturation vapour pressure at 27°C = 3600 Pa.
Use R = 8.3 J K-1 mol-1
The temperature and relative humidity in a room are 300 K and 20% respectively. The volume of the room is 50 m3. The saturation vapour pressure at 300 K 3.3 kPa. Calculate the mass of the water vapour present in the room.
Use R = 8.3 J K-1 mol-1
The temperature and the relative humidity are 300 K and 20% in a room of volume 50 m3. The floor is washed with water, 500 g of water sticking on the floor. Assuming no communication with the surrounding, find the relative humidity when the floor dries. The changes in temperature and pressure may be neglected. Saturation vapour pressure at 300 K = 3.3 kPa.
Use R = 8.31 J K-1 mol-1
A bucket full of water is placed in a room at 15°C with initial relative humidity 40%. The volume of the room is 50 m3. (a) How much water will evaporate? (b) If the room temperature is increased by 5°C, how much more water will evaporate? The saturation vapour pressure of water at 15°C and 20°C are 1.6 kPa and 2.4 kPa respectively.
Use R = 8.3 J K-1 mol-1
A cuboidal container having dimensions 2 m × 1.5 m × 0.5 m holds a mixture of 12 g of He, 36 g of Ar, and 20 g of Ne, If the container is maintained at 300 K, Find the pressure exerted by the mixture (given MHe = 4, MAr = 40, MNe = 20).
In a cubical box of volume V, there are N molecules of a gas moving randomly. If m is mass of each molecule and v2 is the mean square of x component of the velocity of molecules, then the pressure of the gas is ______.
Air separated from the atmosphere by a column of mercury of length h = 15 cm is present in a narrow cylindrical two-soldered at one end. When the tube is placed horizontally the air occupies a volume V1 = 240 mm3. When it is set vertically with its open end upwards the volume of the air is V2 = 200 mm3. The atmospheric pressure during the experiment is 7n cm of Hg where n is a single digit number. n will be ______.
