(Q1)A gas occupies a certain volume at 27c.If it is heated at constant pressure, its volume is exactly doubled at a temperature of. (a)54c(b)219c(c)327c(d)600c (Q2)If the specific heat capacity of water initially is4.2000/kg/k and the difference in temperature of water between the top and bottom of a 210m high water fall is (g=10m/s2) (a)0.05c(b)0.5c(c)1.0c(d)4.2c
[Q1]
Note that for an ideal gas, the volume of the gas is directly proportional to the temperature of the gas (Charles' Law). Just think of it as when you have a balloon of certain volume, and then you heated it (temperature increases), the balloon will expand (volume also increases). NOTE that the temperature must always be in Kelvin units. In the question, the volume is doubled when the temperature is increased; therefore, the temperature is also doubled. We first convert the 27 C to Kelvin (just add 273):
27 + 273 = 300 K.
Then double it:
300 * 2 = 600 K (new temperature)
Since the choices are in Celsius, we convert it to Celsius:
600 - 273 = 327 C
hope this helps~ :)
Q1
p₁V₁/T₁=p₂V₂/T₂
p₁=p₂
V₁/T₁=V₂/T₂
T₁=27℃= 300K
T₂=V₂T₁/V₂ =2 T₁= 600K =327 ℃
Q2
mgh=mcΔT
ΔT= gh/c=10•210/4200 =0.5℃
To answer the first question, we need to use the ideal gas law equation, which states: PV = nRT, where P is the pressure, V is the volume, n is the amount of gas in moles, R is the ideal gas constant, and T is the temperature in Kelvin.
In this case, we know that the volume (V) is being doubled, which means the final volume (V2) is 2 times the initial volume (V1). Since the pressure (P) is constant, we can rewrite the equation as: V1/T1 = V2/T2.
We are given that the gas occupies a certain volume at 27c. To convert Celsius to Kelvin, we add 273 to the temperature. So, T1 = 27 + 273 = 300K.
Now let's calculate T2: V1/T1 = V2/T2
Since V2 = 2V1, we can substitute and solve for T2:
V1/T1 = 2V1/T2
T2 = 2T1
T2 = 2 * 300K = 600K
So, the answer to question 1 is (d) 600c.
To answer the second question, we need to use the equation Q = m * c * ΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
We are given that the specific heat capacity of water initially is 4.2000/kg/K.
Given that the difference in height is 210m, and the acceleration due to gravity (g) is 10m/s^2, we can calculate the change in temperature (ΔT) using the formula: ΔT = Δh / (g * c), where Δh is the change in height.
ΔT = 210m / (10m/s^2 * 4.2000/kg/K)
ΔT = 210m / 42J/(K*kg)
ΔT = 5K
So, the answer to question 2 is (a) 0.05c.