Given Information:
Diameter of spherical cell = 0.040 mm
thickness = L = 9 nm
Resistivity = ρ = 3.6×10⁷ Ω⋅m
Dielectric constant = k = 9.0
Required Information:
time constant = τ = ?
Answer:
time constant = 2.87×10⁻³ seconds
Explanation:
The time constant is given by
τ = RC
Where R is the resistance and C is the capacitance.
We know that resistivity of of any material is given by
ρ = RA/L
R = ρL/A
Where area of spherical cell is given by
A = 4πr²
A = 4π(d/2)²
A = 4π(0.040×10⁻³/2)²
A = 5.026×10⁻⁹ m²
The resistance becomes
R = (3.6×10⁷*9×10⁻⁹)/5.026×10⁻⁹
R = 6.45×10⁷ Ω
The capacitance of the cell membrane is given by
C = kεoA/L
Where k = 9 is the dielectric constant and εo = 8.854×10⁻¹² F/m
C = (9*8.854×10⁻¹²*5.026×10⁻⁹)/9×10⁻⁹
C = 44.5 pF
C = 44.5×10⁻¹² F
Therefore, the time constant is
τ = RC
τ = 6.45×10⁷*44.5×10⁻¹²
τ = 2.87×10⁻³ seconds
Answer: 80J
Explanation:
According to the first principle of thermodynamics:
<em>"Energy is not created, nor destroyed, but it is conserved." </em>
Then this priciple (also called Law) relates the work and the transferred heat exchanged in a system through the internal energy
, which is neither created nor destroyed, it is only transformed. So, in this especific case of the compressed gas:
(1)
Where:
is the variation in the internal (thermal) energy of the system (the value we want to find)
is the heat transferred out of the gas (that is why it is negative)
is the work is done on the gas (as the gas is compressed, the work done on the gas must be considered positive )
On the other hand, the work done on the gas is given by:
(2)
Where:
is the constant pressure of the gas
is the variation in volume of the gas
In this case the initial volume is
and the final volume is
.
This means:
(3)
Substituting (3) in (2):
(4)
(5)
Substituting (5) in (1):
(6)
Finally:
This is the change in thermal energy in the compression process.
Answer:
Explanation:
Expression for velocity of wave produced in a hanging wire can be given as follows
Velocity v = 
where T is tension in wire and m is mass of wire per unit length.
In the given case
T = Mg + mg
= Mg
neglecting weight of rope
mass of the rope per unit length
= m / L
Velocity of wave
= 
= 
The independent variable is the type of fuel used and the dependent variable is the speed of the race car. The independent variable could be changed through the experimental process to see its relation with the dependent variable<span>. The dependent variable is the result of the independent variable changes.</span>