Answer:
Q = 62 ( since we are instructed not to include the units in the answer)
Explanation:
Given that:



Q = ???
Now the gas expands at constant pressure until its volume doubles
i.e if 
Using Charles Law; since pressure is constant




mass of He =number of moles of He × molecular weight of He
mass of He = 3 kg × 4
mass of He = 12 kg
mass of Ar =number of moles of Ar × molecular weight of Ar
mass of He = 7 kg × 40
mass of He = 280 kg
Now; the amount of Heat Q transferred = 
From gas table

∴ Q = 
Q = 
Q = 62 MJ
Q = 62 ( since we are instructed not to include the units in the answer)
Answer:
1090 Steel >1040 Steel > Pure aluminium >Diamond.
Explanation:
Toughness:
Toughness can be define as the are of load -deflection diagram up to fracture point.
Modulus of toughness can be defines as the area of stress-strain diagram up to fracture point.Modulus of toughness is the property of material.
So the decreasing order of toughness can be given as follows
1090 Steel >1040 Steel > Pure aluminium >Diamond.
The weight of the specimen in SSD condition is 373.3 cc
<u>Explanation</u>:
a) Apparent specific gravity = 
Where,
A = mass of oven dried test sample in air = 1034 g
B = saturated surface test sample in air = 1048.9 g
C = apparent mass of saturated test sample in water = 975.6 g
apparent specific gravity =
= 
Apparent specific gravity = 2.88
b) Bulk specific gravity 

= 2.76
c) Bulk specific gravity (SSD):


= 2.80
d) Absorption% :


Absorption = 1.44 %
e) Bulk Volume :


= 
Answer:
R = ![\left[\begin{array}{ccc}1&0&0\\0&cos30&-sin30\\0&sin30&cos30\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%26cos30%26-sin30%5C%5C0%26sin30%26cos30%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}cos 60&-sin60&0\\sin60&cos60&60\0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dcos%2060%26-sin60%260%5C%5Csin60%26cos60%2660%5C0%260%261%5Cend%7Barray%7D%5Cright%5D)
Explanation:
The mappings always involve a translation and a rotation of the matrix. Therefore, the rotation matrix will be given by:
Let
and
be the the angles 60⁰ and 30⁰ respectively
that is
= 60⁰ and
= 30⁰
The matrix is given by the following expression:
![\left[\begin{array}{ccc}1&0&0\\0&cos30&-sin30\\0&sin30&cos30\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%26cos30%26-sin30%5C%5C0%26sin30%26cos30%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}cos 60&-sin60&0\\sin60&cos60&60\0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dcos%2060%26-sin60%260%5C%5Csin60%26cos60%2660%5C0%260%261%5Cend%7Barray%7D%5Cright%5D)
The angles can be evaluated and left in the surd form.