Advertisements
Advertisements
Question
An inflated rubber balloon contains one mole of an ideal gas, has a pressure p, volume V and temperature T. If the temperature rises to 1.1 T, and the volume is increased to 1.05 V, the final pressure will be ______.
Options
1.1 p
p
less than p
between p and 1.1.
Advertisements
Solution
An inflated rubber balloon contains one mole of an ideal gas, has a pressure p, volume V and temperature T. If the temperature rises to 1.1 T, and the volume is increased to 1.05 V, the final pressure will be between p and 1.1.
Explanation:
According to the equation of ideal gas, PV = nRT
P = pressure
V = volume
n = Number of moles of gases
R = gas constant
T = temperature
Thus we have to rewrite this equation in such a way that no. of moles is given by,
`n = (PV)/(RT)`
The number of moles of the gas remain fixed, hence, we can write
`(P_1V_1)/(RT_1) = (P_2V_2)/(RT_2)`
⇒ `P_2 = (P_1V_1) (T/(V_2T_1))`
= `((P)(V)(1.1T))/((1.05)V(T))` .....`[(P_1 = P),(V_2 = 1.05 V and T_2 = 1.1T)]`
= `P xx ((1.1)/(1.05))`
= `P(1.0476) ≈ 1.05 P`
Hence, final pressure P2 lies between P and 1.1P.
APPEARS IN
RELATED QUESTIONS
The pressure of an ideal gas is written as \[P = \frac{2E}{3V}\] . Here E refers to
Which of the following quantities is the same for all ideal gases at the same temperature?
(a) The kinetic energy of 1 mole
(b) The kinetic energy of 1 g
(c) The number of molecules in 1 mole
(d) The number of molecules in 1 g
At what temperature the mean speed of the molecules of hydrogen gas equals the escape speed from the earth?
Use R = 8.314 JK-1 mol-1
An ideal gas is trapped between a mercury column and the closed-end of a narrow vertical tube of uniform base containing the column. The upper end of the tube is open to the atmosphere. The atmospheric pressure equals 76 cm of mercury. The lengths of the mercury column and the trapped air column are 20 cm and 43 cm respectively. What will be the length of the air column when the tube is tilted slowly in a vertical plane through an angle of 60°? Assume the temperature to remain constant.
Using figure, find the boiling point of methyl alcohol at 1 atm (760 mm of mercury) and at 0.5 atm.
Compare the rates of emission of heat by a blackbody maintained at 727°C and at 227°C, if the black bodies are surrounded by an enclosure (black) at 27°C. What would be the ratio of their rates of loss of heat?
The power radiated by a perfect blackbody depends only on its ______
Why the temperature of all bodies remains constant at room temperature?
If the density of nitrogen is 1.25 kg/m3 at a pressure of 105 Pa, find the root mean square velocity of nitrogen molecules.
Explain in detail the kinetic interpretation of temperature.
A molecule consists of two atoms each of mass 'm' and separated by a distance 'd'. At room temperature the average rotational kinetic energy is 'E', then its angular frequency is ______.
An ideal gas in a container of volume 500 cc is at a pressure of 2 × 105 N/m2. The average kinetic energy of each molecule is 6 × 10−21 J. The number of gas molecules in the container is ______.
The molecules of a given mass of a gas have root mean square speeds of 100 ms−1 at 27°C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127°C and 2.0 atmospheric pressure?
A gas mixture consists of molecules of types A, B and C with masses mA > mB > mC. Rank the three types of molecules in decreasing order of average K.E.
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, KP are related as ______.
When the temperature of an ideal gas is increased from 27°C to 227°C, its speed is changed from 400 ms-1 to vs, and Then vs is ______.
When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is n, then the frequency of the kinetic energy is ______.
If a = 0. 72 and r = 0.24, then the value of t is ______.
Show that the average energy per molecule is directly proportional to the absolute temperature ‘T’ of the gas.
